Without water mosquitoes cannot reproduce. It stimulates the development of eggs into larvae, and provides the medium in which the larvae swim and feed on algae and organic debris until they are ready to transform into adult. So some mosquitoes lay their eggs in water, and others in places where there will eventually be water.
In central Australia, where rain is very infrequent, Aedes mosquitoes (carriers of yellow fever), lay their eggs in pools after a downpour. The pools soon evaporate and the eggs may stay dormant for years until it rains again. Then the mosquito life cycle starts anew as if no time had elapsed.
The eggs of other species of mosquito may not need to wait so long, but they are certainly capable of surviving droughts and similar harsh conditions, such as Arctic winters. With all water frozen, an Arctic winter has the same effect as a drought. But the Arctic Culex mosquitoes (carriers of viral encephalitis) are some of the most successful breeders. After nine or ten months of suspended animation in ice, their eggs are released in the summer melt-waters. They float on the water in rafts of about a hundred, turn into larvae, then pupate. In a few days, the summer air is thick with adult mosquitoes.
Mosquitoes are the scourge of Arctic animals that are trying to breed during the brief summer. One of the commonest causes of death in newborn mammals and birds is loss of blood from innumerable mosquito bites.