Yes, this is totally correct and I agree full-on with what you're saying. Unfortunately we have to put up with explaning a lot of stuff to people who misinterpret what's actually going on.
Everyone seems to use the "it's cold in _____ location, therefore there is no global warming". The answer of course is simple: It's called global warming (or better yet, climate change) for a reason. Does that location on its own adequately represent global weather? I think not.