What I've always been told is that Icelandic winter danced around the freezing point enough that mosquitos weren't able to overwinter effectively. The larvae would hatch prematurely thinking it was spring and be killed by another freeze before they could get a foothold.

That hypothesis relies on a pretty careful climatic balance though. Clearly it's hit a point where some parts of the country can now support endemic populations. My wife swears she was attacked by them when I took her to meet my grandparents a couple years ago, which I was quite resistant to believing at the time vs the similarly annoying midges. Maybe she was right?