There are tonnes of sharings online on what to pack when heading to Iceland from international travel bloggers. More often than not, the brands mentioned are not that easily within reach for purchase here in Singapore, or in Asia perhaps.
Below I will list some items I managed to assemble for the trip from Singapore's shops—offline and online.

You know how things can get too cold for comfort.

We are so used to the hot humid temperatures of Singapore that heading to Iceland actually puts me on a brain freeze mode. Temporary at least.

Prelude

When I was there from end November to beginning of February, strictly speaking, it wasn't that freezing butt cold. It did not even hit minus. The most we got was 0degC. As night fell deeper, the temperature could have dipped to minus but we were mostly already in our accommodations. Night falls quickly at around 4 pm during winter. In the and basically there are no forms of shopping or entertainment around ( I am referring to areas outside of Reykjavik such as Vik. Reykjavik being the capital is an exception,)

Nevertheless, when in preparation, we prepared with -15deg in mind. Everything we bought was to suit that possibility of a temperature, As I have learnt since other areas along the Artic Circle be it in Canada or Sweden are much colder in comparison to Iceland in the same period. I have been monitoring temperatures in Reykjavik since my return. For the whole month of December, the lowest I saw was probably -4degC. From the words of my friends who happened to be in Yellowknife, Canada she reported a whopping -15degC ! (And she was also able to spot lovely Aurora)
Conclusion: Iceland is not that freezing icy cold as its name sounds.

Okay, I digress. Back to packing, I at least was super intolerant of the cold and had trouble deciding what to buy for inner and outer.

Top

Here's what I found at ColdWear Singapore shops.

For me, I wore Uniqlo's Heattech Innerwear ( Note: There are 3 grades: Ultra warm, Extra warm and 'Regular') I had the normal version and layer on with another polyester thermal,  These 2 layers basically kept me comfortable throughout the trip.

I had not tried the Extra Warm Heat tech but I believed it might have been sufficient as the only inner wear layer if the temperature is up to zero till -10degC. ( Psst: Uniqlo always has sales online and offline so stock up for your next trip! Especially since the December period is ending.)

 Mid-Layer
 Once again Uniqlo's Heattech fleece turtleneck came in handy and of course any of your long sleeved wool or fleece wear will be good. The tip is effective layering with soft materials.
Do avoid cotton as it does not retain heat and if wet, will cause you to be freezing cold, fast.

I had on 2 layers in the middle — the turtleneck and a flannel shirt that's good for layering and looks nice enough as an outerwear if necessary.

Outer-Layer

The Down coat was the tricky part. Having no experiences at all in heading to the winter lands, I had a hard time finding the right down at the right price. But of course, eventually, I found choices in Uniqlo as well as in WinterTimes at Singapore IMM's outlet ( shopping mall) which has some great ongoing discounts.
The thumb rule is this: Choose a jacket that's waterproof with at least 80% down as per stated on the material label. Without down, which is essentially feathers from goose or ducks, you can't be kept warm. 90% Down is best for up to -10degC.

  The Uniqlo Seamless Down Short Coat is an awesome choice. Don't say I never share.

With that, you will be snugly warm.
Trendy trench coats come without down and are rendered useless in these weather.

Bottoms

Inner-Layer

 I had on a pair of Fleece-lined leggings which I bought from Qoo10 and found it warm and snug. Inclusive of shipping, it costs a total of $12.90 and you can get multiple pairs for regular change. This can actually function as a pair of legging on its own at a higher temperature of 5 to 0degC.
For me, I wore it as an inner layer. 

Outer-Layer

The inner fleece-leggings was paired with thermal pants from  Uniqlo Heattech High rise legging pants which come lined with fleece for extra warmth too. 2 layers was all I needed in Iceland. I had tried just wearing the Uniqlo pants on its own but it proved to be not sufficient as cold air and the wind would still seep in.

Experience

Yes, I have to praise the Uniqlo legging pants for practically being waterproof. Case in point, we were totally drenched in the heavy downpour on one of those days. Heavy being an understatement but we had to get out regardless. We were there at Skógafoss and there was no returning on another day. If not ever. So, we got out braving the huge downpour to take those photos. 
Down jacket drenched, hair drenched, shoes slippery over the melting snowy rocks. Alas, when I checked on the pants, my legs were dry and the interior not wet. 
Case proved.

Jeans?

I had read numerous reviews and advice on not to wear jeans to a place which is wet and cold. I totally agree as jeans are cotton and if you come in contact with ice or snow, say you play in them, then your butt would be freezing cold and your jeans will take forever to dry. However, that say, if you know that the itinerary for your day is mainly walking in the city or shopping around, then jeans will be fine. 

It can get a bit bulky with the layerings so I would advise you to up one size for the outer pants and down jackets.

Hand Warmers

The need for heat pads is real. If you really have to downsize to the essential, get those hand warmers. Forget about body or toes heat pads. My pals and I discussed what kind of heat pads do we really need? Handwarmers for me, win hands down and they turned out also to be the cheapest too. Enuff said.

Now for the big secret. 

Where to get warm 'effective' heat pads?

OG. Yes. Head to People's Park OG ( Singapore's shopping mall) and sweep away.  

Definitely, works in providing adequate warmth and heat.

This is the packaging.
Alternatively, Kiribai warmers can be found on Amazon too.

 Kiribai is the brand and you can find them at the winter wear section in OG. When I returned from my trip in early December, the hand warmers were all gone. Left only with the body/ feet heat pads.

Okay, so maybe it's not that big of a secret and everyone knows about the effectiveness of these pads.

I had tried the $2 heat pads over in Iceland and it did not work.  I would strongly recommend you to get Kiribai's hand warmers.

 Keeps you warm and happy. 

Accessories

Of course, there are the others like a touch-sensitive pair of gloves, scarf etc.

Beanie/knit cap ( most preferably lined with fleece). For me, I think having a hood on the outer down jacket is more than suffice for the temperature of about 3 to -1degC when I was in Iceland.  Of course for aesthetic/photo taking purposes, a cap will still be nice.
For even colder temperature below -5degC you will possibly need a beanie to keep your ears warm in addition to the hood on your jacket.

Wool socks are strongly recommended to eliminate the moisture to keep your feet warm.  Just to share I purchase wool socks from Qoo10, same seller as the thermal pants and it was good. I was basically kept warm and at $2,50 it's cheaper than retail.  Here's the wool socks link.

Footwear

This was another headache. For me, the winter noob. :)
There are definitely numerous hiking boots better and more withstanding but I am just going to share where I got in the end.
Timberland was my choice eventually and I had the Timberland Women's Nellie Boots.

Warmth: Definitely kept me warm from the cold and moisture.
Waterproof: After a day out drenched in the rain, the exterior was wet but my feet was kept dry and snug. Subsequently, it dried out pretty well on the exterior too.
Thumbs up for the premium Nubuck leather!
Weight: Slightly heavier and take some time getting used to for walking, even with its anti-fatigue midsoles function. The <Authentic Rolls-up> is definitely a lighter version.

Traction: Slight disappointment but I understand the soles were not anti-slip, to begin with for the Nellie Boots.
 With the rugged rubber soles, one would have thought that the traction will be great. True, it was all pretty well till I come across the ice on stones/rocks. Totally slippery with no grip.
 Of course, I understand these are not spikes-for-ice-kind of shoes but even on watery wooden planks, it proved to be quite slippery and I wonder how possible it is to use for hiking.
 I will probably try again for hiking in the future.

Disclaimer: This is not an advert for any of the brands above and I had purchased all the above products mentioned and tested them out in Iceland.

The above items are of course, not exhaustive. If you do have more to share, comment below and let us know.
Thank you for reading and I hope you will find it easier to shop for your Arctic trip!