What is the climate of a wetlands biome?

This is going to be different dependent upon where you live. For example there are wetlands found along streams and marshes at 100 ft elevation and wetland regions surrounding alpine lakes at 9000 ft elevation. Wetlands are ecosystems that surround rivers, streams, and marshes. If there is a college, museum, or other similar facility near you you can do a website search for wetland characteristics and get a lot of that information for your local area.
Wetlands are not usually considered biomes, although if that is what your teacher wants to call them, its best not to argue (they are habitats or ecosystems). An example of a biome would be grassland, tiaga, tundra, tropical rain forest, deciduous rain forest, deciduous rain forest, etc.

Wetlands are all over the world.  Different kinds in different places.  Pick one and go with it.