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what mounts would i need for a snowmobile and bow and arrow
depends on the position you want to install the camera. If you want it facing you, there is a mount for the handle bar, and you can rotate the camera facing forward or backwards.
I wouldn't do suction mount, due to the extreme vibration on the snowmobile, and jumps, etc.
I didn't understand exactly if you want to mount the bow on the snowmobile, or the camera on the bow, so here are the 2 possible answers I have:
For bow and arrows on the snowmobile:, depends on the model you have, and how can you fit it either on the handle bar, or on the cargo area in the back of your snowmobile. Maybe something on the style of the Kolpin Rhino Grip Xl Rack/Handlebar Mount Kolpin Rhino Grip Xl Rack/Handlebar Mount look up for similar mounts that can fit your rig.
Now, if you want to mount the camera on your bow.... I think the best solution is a wrist mount you put on your left arm (if you are right handed). I don't like the idea of mounting something on the bow, since it's going to change the way the bow "resonates" and change the balance on it.
With the wrist mount, you can get the camera facing forward and aligned with your arm and your line of sight...
Good luck!