I’ve spent quite a lot of time on snow and in my opinion being warm and dry is the key to having fun. There is nothing worse than being cold and wet and having snow where there isnt meant to be snow – i.e. inside your jacket or down you trou becuase your jacket hasn’t kept it out. Ski/Board jackets are cut differently and are designed to keep snow out – a powder skirt makes a hell of a difference.
If you’re new to ski then you are going to be spending a certain amount of time in the snow, either sliding or sitting putting on skis or board.
I’ve boarded in a t-shirt before, in April, in Mayrhofen, but in dec or Jan in the Northern Hemisphere than I’d plan for it gettign to -20C maybe more with wind chill. In canada in Jan my beard froze to the collar of my jacket.
Seriously, good socks, good gloves will make a lot of difference but I would at the very least go to TK Maxx and buy a proper 15000/15000 min waterproof/breathable snowjacket with a powder skirt – I bought a TENSON a couple of years ago for about 40GBP, the Tenson I had before that from a skishop cost me 200+gbp and last 4 or 5 years.
Not worth ruining a holiday by ending up cold and damp or being fleeced in resort.
Where are you headed anyway?
EDIT: Re: Helmets – I haven’t worn one up until now but when I go next I’ll definitely be getting a proper boarding lid, seen a couple of mates have bad injuries and some that haven’t recovered from them. Even a cheapo one would be better than a MTB helemet as they offer more protection to the rear of the head usually.