Nosquitos themselves can't survive when it goes below freezing, but sadly their eggs are nearly indestructible. Siberia, Alaska and the northern parts of the Nordics are absolutely plagued with them in the summer, since snowmelt creates huge amounts of stagnant water that melts the eggs in a perfect habitat for breeding.
Shocking considering how cold it gets there. It's cold and dry and windy where I live, and there are nearly zero skeeters. I spend most of my afternoons on the porch, and I've been bit twice all summer. But this tracks with what I've heard from campers and hikers in that region. You wake up and your tent is covered in the little bastards.