First of all i think you should stop judging people, perhaps moshiach isn’t here because of people like you who have nothing to do with their time than accuse normal men and women on the street of being ba’alei gavoh.
Rant over. The reason why it’s not osur because of beged ish, is, as rashi on the pasuk of ‘lo yilbash’ says that cross dressing is only osur when it’s done in a way that could lead to wrongdoing. Here, it is merely being done due to inclement weather conditions, or perhaps because they’re balei gavoh, as you suggest, but certainly not to get upto mischief.
Hope this helps!