I have an advanced PADI license and have been diving in Silfra twice myself.
Being cold is not going to be a problem, or at least it wasn’t for me.
The water is cold, but you don’t really notice it that much because you’ll be given a super warm overall that’s like a thick sleeping bag, underneath your drysuit - that will keep you dry the whole time. You’ll also get wetsuit gloves and a hoodie. You’ll mostly notice the cold on maybe your cheeks, I don’t really remember the cold much. I went with Scuba Iceland and they give you some hot chocolate and cookies after your dive as well!
The water is so cold and clear that you can both drink it, and have visibility of around 120 metres - it’s simply stunning Plus, they offer two dives, and I totally recommend doing both dives, even though you’ll be seeing the same location again, you may have some trouble adjusting to the drysuit in your first dive (at least I did) and by the second dive you should have the hang of it and be able to enjoy the scenery more.
Take note though that wearing a drysuit is much more bothersome than wearing a wetsuit or just a regular swimsuit, you’ll need heavier weights and when you’re on land everything’s just a little harder than usually. The short walk you need to take after the dive feels much longer than it actually is when you’re carrying all that extra weight! This is what was a bigger problem for me, rather than the cold
Silfra is one of the best dive sites in the world, so any qualified diver coming to Iceland shouldn’t miss out on it in my opinion!