I've used both kinds of helmets and right now I'm using a dirt bike helmet. Dirt bike helmets don't fog up as easily. If its a warm day you have an alternative to sweating to death because your helmet has ventilation. In the cold dirt bike helmets require something like a ski mask so your chin and neck don't freeze.
Snowmobile helmets can fog up if you don't have an electric helmet. But they are warmer. But on a warm day when you start to sweat you really don't have a way to cool down other than putting your visor up.
Those are the pros and cons that I know of for the two helmets. I use a dirt bike helmet because I have a dirt bike and I don't wanna spend the money on a snowmobile helmet.
Oh, and dirt bike helmets look sick. :P
Ya I'd say its official now, winter in Connecticut sucks. Rain/sleet/freezing rain in winter??
"Life moves pretty fast. If you don't stop and look around once in a while, you could miss it."
1996 Formula SLS
1989 Jag 440 AFS
1986 Citation LS
If you are talking about full face helmets with raisable shields, the snowmobile helmets generally come with a dual pane shield that is supposed to reduce fogging.
Snowmobile helmets generally have more closable air vents so that you can adjust airflow depending on the temperature.
Some of my riding buddies have gone to a motocross type helmet with goggles instead of a shield, and some of them swear by them (and some of them swear at them)
On the VERY cold days, you really want to avoid having any exposed skin, so if you go with the Motocross/goggles solution, you want to make sure the goggles fit tight in the helmet and that you have some nose and lower face protection.
I personally use a BRP Modular 2 with a heated shield. I don't have to plug in the shield except for the very coldest days. But, the other guys are right, there is nothing worse than having your shield frost over so that you can't see clearly, especially at night.