Mosquitoes do go away during the winter months when it turns really cold.
Mosquitoes don't actually completely die though during cold weather but instead they go into hibernation and are less active during the winter months.
Once spring and summer arrive then the mosquitoes come out of hibernation and that's when you see the mosquitoes again.
Mosquitoes are still out there in the winter but they're just hibernating and are less active during cold weather.