Do wasp live in cold weather?

No. They all die in late summer but the queen survives in a state of semi-hibernation to restart a colony in the spring.

This is true of most social wasps. In some colonies, the queen dies and a new queen emerges in the spring. In solitary wasps, such as the mud-daubers, potter wasps, ichneumonids, and relatives, the adults generally die in colder climates and are replaced by newly hatched adults in the spring. In more tropical climates, the individual nature of the wasps allows them to hatch and mate throughout the year succumbing to death by predation, accident, or old age.