In national parks, snowmobiles have no place. Their paths inadvertently can cut into young saplings and smaller plants, weakening the forest's potential growth come spring time. Their exhaust also has a negative effect on the air, poisoning the flora and fauna as they try to breathe. Overall, the fun isn't worth the potential environmental damage.
There is no need to ban snowmobiles from the US national parks; all that needs to be done is a set of strict rules that are just as strictly enforced. Yes, driving a snowmobile CAN be dangerous and it CAN damage the park. That's why people need to be told exactly how they are expected to operate a snowmobile in a park and what will happen if they violate the rules.