One of my best friends wears a downhill bike helmet when we go riding 4 wheelers. I used to think he was crazy and it wasnt enough protection.
But this summer riding the dunes when it's really hot out I am riding around without chest protection elbow pads etc because its just too friggin hot out.
Sometimes I would only wear an open face helmet (not a bright idea).
If it was super hot I wouldn't wear a helmet, but would just ride different.
I'm not doing backflips over sand dunes, just cruising around doing doughnuts and stuff.
With snowmobiling i'm not going to be doing crazy chute hill climbs and backflips, just getting to the spot, tandeming up and snowboarding. I quit wearing a helmet with snowboarding when I stopped riding ice.
In short, if i'm not pushing it hard I think I can trust my judgment with just a fullface mountain bike helmet. The thing about riding anything with handlebars is you have the suspension and your arms to take up ALL of the shock. look at all that stuff bolted to the handlebars, grill ruiners.
TLDNR
My personal bottom line is - if it breathes well, not too hot and is very light I am alot more likely to wear it. Simple.
I'm willing to bet my brain that I wont be hitting trees at 50mph on a snowmobile that I just paid 4k to get fixed.