The brand is not so important. The quality of the clothes is important. Of course, brand may be an indicator of quality. But just go to any normal sports/outdoor store in Iceland or your home country, and it's not too hard to judge the quality. If you go to a known sports/outdoor store in Reykjavik, for example, they're almost certainly not gonna sell low quality clothes. And the staff will be able to advise you. So stop worrying about the brand thing.
I am very cold sensitive person.
I grew up in a quite cold country, and I've gone skiing, running, walking, playing, hiking, bicycling, etc. in the mountains there and in temperatures as cold as around -20 Celsius as a part of my childhood and youth. The single best tip I can give you is to wear wool. There is nothing like wool to keep you warm in a tough winter.
Here is a garment anyone living in a country like Iceland is familiar with. It's a tight fitting woolen garment called woolen long-johns. Any sports/outdoor store in any cold place will have it.
On top of this, you can wear normal clothes like pants and a winter jacket, etc. If you're still cold, put on another layer of wool, like a woolen sweater or even pants. You'll be ready to spend the whole day outdoors in Iceland.
Now, you may be thinking that wool next to your skin is itchy. It is, to some degree, but these days they have ways to treat the wool to make it less itchy. Also, you get used to it. I personally prefer a little bit of itching to being cold. If you cannot stand wool directly on your skin, however, there are synthetic alternatives. They look somewhat similar, but they are not actually wool. If doing this, compensate by wearing a thick woolen sweater and woolen pants on top of it.
Avoiding wind is also very important. Make sure your jacket is windproof. Windproof pants also exist.
Rain is another thing that can easily spoil your trip, so make sure you pack a solid raincoat and rain pants.
It's extremely important to keep your feet warm. Pack woolen socks. You can wear them directly on the skin or outside cotton socks if you prefer. Keep solid boots and make sure you have rain boots in case it gets wet. Few things are worse than wet feet.
Again, forget about the brands. Go directly to the sports/outdoor store and judge the quality there.