i have never had a problem with cold weather and stereo equipment. sometimes when i jump into my car and start it when there is snow on the back i throw some bass disc in to shake some snow off cause im lazy.
i have had subs that needed to warm up so assume the same can be said for tweets, its probably less noticable as the tweeter itself moves a lot less than a sub...my only concern would be why just one of them?
someone over at toyotanation.com said it could be a cold soldering joint? at the tweeter.. basically he said try and solder it good and see if it helps.. and if not it could be internal o_O