To my knowledge, titles are not issued for snowcats. They convey ownership of a Motor Vehicle, as US DOT determines it, which is to say it must have been built to operate on-road. But that's where it gets unclear, since registration for on-road operation is the responsibility of the state/s.
Titling is a federal issue, so in theory it should be uniform. But that's not to say that one hasn't slipped through the cracks. I know of a guy who's got a title for his halftrack, and it ain't legal on the roads here in Wis.
Trailers often have titles because they are assumed to be on-road vehicles. They're likely handled differently from snowcats.
I believe VINs can only be assigned by NHTSA, State Patrol officers, and perhaps Registered Importers.
Best off addressing your question to your local DOT/DMV. It's also possible that your DNR may have authority over the matter, since it's an off-road vehicle.