Please synonym air-conditioning and cooling. Because of varying climates, I think it's appropriate to treat different environmental conditioning elements separately (i.e. heating, cooling, (proposing tag) [ventilation]). So in this sense, air-conditioning and cooling should be synonyms. If something less specific is meant by "air-conditioning," then the precise tag should be used.
It's potentially a good idea.
It does set me wondering about what people mean by these terms. As gerrit mentions in a comment, cooling can refer to refrigeration and freezers.
Furthermore, air-conditioning includes dehumidification as well as cooling; it can include humidification and air-filtering too.
So, we've got a bunch of topics with partially overlapping tags (where the tags already exist, or could do):
I'm minded, for now, to leave things as they are, watch how they evolve, and come back to it when we've got more questions on this family of tags, to see if there's a clearer pattern. And I'm also happy to go with what the community decides, if we get a clear signal before then.