The winter is a lovely time to crossdress, when layering, coats, boots, gloves, and other accessories let you be more expressive of yourself.
He probably hides it because he's ashamed of himself and probably hates himself for it because he can't control it and society tells him that he's a wuss, less of a man, a ->-bleeped-<-got, whatever, because of it. He's afraid of losing you, that you'll leave him because he's a pervert, or not manly, or whatever.
You didn't really elaborate on the crossdressing. The whole thing is quite complex. There are those who dress for sexual satisfaction, those who dress to pass, for comfort, what have you.
I originally started sexually because I wasn't grown enough to understand and separate sexuality from gender. Being TG, i certainly enjoy it sexually because hey, women like sex too. Yes, I've love to wear some lingerie with someone, but putting on a pair of panties to go to work doesn't turn me on, it's just part of whatever i'm wearing for the day.
I present male...well, androgynously at this point I suppose, when I'm not at work I crossdress in womens 3/4ths, tees, jeans, slacks, coat, and such, I pass quite often, but I'm not trying. It makes me feel better to wear the clothes I do because a) they fit better and b) it feels right. Mens clothing is bulky and feels wrong. I'd crossdress fulltime at work but when I buy nice clothes that are work appropriate I don't want to ruin them by wearing them to work.
Crossdressing is usually a sign of a deeper problem. A lot of crossdressers recognize gender dysphoria after a while. Sometimes a cigar is just a cigar of course.
The thing is that, no matter how supportive you are, he's probably got a lot of internal fears and loathing to deal with. It's a terrible insecurity and really tragic. Educate yourself with material around here and online and work slowly. He'll cherish you forever if you get past the hurdle and are still a loving couple.