This checklist will give you an idea of what you'll need for your trip to Iceland, this is based off my experience of visiting in February. February is at the height of winter where you will expect a lot of snow and for it to be very cold. However relying on the weather apps is no good, so making sure you're covered for all bases is the best idea and I aim to help you with that. I have three categories that are worth mentioning, clothing and footwear, accessories and equipment.
Clothing and footwear -
My packing list on the clothing front was very minimal as I went for practicality over style due to how cold I knew it would be. I would make more an effort at night to wear something a little more dressier but in the day when doing excursions and activities I planned for warmth and comfort.
Thermal base layers, this will include anything from tops, leggings to socks. These are the most important layers as they need to be skin tight to lock in any heat.
Jacket, in my case I took two puffer jackets. These were a life saver as they didn't allow any cold to pass through, ensuring I stayed warm all day.
Over trousers, these were the best things to bring. For rainy days especially, you just slip them over whatever trousers you have on and they will not only protect them if you're doing an activity but they are waterproof and an additional layer is always ideal.
Swimsuit, this is a must need for trips to Blue lagoon or Sky lagoon (or any thermal spa of your choice)
Trainers, these were my evening shoe of choice as well as my travel shoe.
Winter boots, these were my go to shoe for the days especially during excursions. I bought this pair from hunter which were waterproof/resistant, non slip and could handle up to -15 degree temperatures.
Flip flops, these are also to take to the lagoons so that you're not having to walk around barefoot.
Hand warmers & foot warmers
Tripod, this will come in handy when you go to see the northern lights as you can keep your hands in your pockets and also set up your phone or camera so that your images aren't shaky due to the long exposure.
Waterproof phone case, this was specifically taken to use at blue lagoon just as a precaution, they do sell them there but the price is hiked up so if you feel you would like to use one to protect your phone you're better off bringing one with you.
Ice grips (Crampons), these are spiked frames that you attach to your shoes/boots especially in icy conditions as extra grip. I only used these once on my trip but if you feel you may encounter very icy locations during your visit these are a good addition.
That would complete everything I took on my trip and I hope it serves as a guidance on what you can also take on your future trip to Iceland!