Check out this brief read: http://www.livestrong.com/article/184657-differences-between-ski-skate-helmets/
I'm assuming you're wearing a hat underneath your helmet? Depending on what's between your head and helmet you may sacrificing fit, which sacrifices safety.
Basically, the primary difference seems to be from multiple or single impact design. Skiing falls often involve tumbling, rolling, bonking, crashing, sliding............ so snow helmets are designed with that in mind. While, skate/bmx helmets are designed for the big primary impact of the crash.
The biggest and most important thing is the helmet certification of safety which comes in the form of a rating, generally ASTM.
I know a lot people wear skate/bmx helmets on snow, but my personal advice to you would be to get a snow specific helmet.