Technically, no. “Tundra” has the specific meaning of being a place where limited sunlight and temperature limit tree growth.
But all tundra on this planet is frozen for a pretty large part of the year and all, or just about all, has permafrost. There’s nowhere that is tundra that is not frozen a lot. It’s theoretically possible to have tundra that isn’t generally frozen, but we don’t have any examples. So PRACTICALLY speaking, it’s sort of redundant.