Yes, the recent stretch of cold weather will no doubt kill some mosquitoes. Those that came out of hibernation during some of our milder February days have fallen victim to the cold.
However those mosquitoes that remained hibernated will survive. Not only that, any eggs that were laid by previous mosquitoes will also survive.
So despite the cold, we'll still need to take precautions this spring and summer to avoid becoming the victim of a thirsty mosquito.