Most amphibians can breathe both through cutaneous respiration (through their skin) and buccal pumping - though some also retain gills as adults. Some aquatic salamanders (and all tadpoles) have gills and can breathe underwater thanks to them. The Mexican axolotl, for example, never loses its gills.
In short, weather is to describe the day or week (short period). . As for the climate, it is to describe the year or (a long period), for example, the climate of the winter season is cold.