As I understand it, snowmobile trails generally are not open to any motorized traffic during non-winter months.
That’s mostly because in NY all snowmobiles are required to have insurance, and also DMV collects portion of registration dedicated to a trail fund. So they (you, maybe someday me) are just much more well organized and powerful in our bureaucratic process of gov;t.
That said, they also happen to be comprised of existing public/private land, some of which does allow for other traffic, but not most, and some of which gets used for it anyway (noticed closed gates with well tread bypass).
"Areas where this activity is permitted are very limited
with almost all existing trails on private land. Despite
that, there are a number of organizations that support
this activity"
https://parks.ny.gov/documents/recreation/trails/StatewideTrailsPlanAppendixG.pdf
Personally I have been trying to push on whatever buttons I can find to get more support on public land for responsible use, but am getting a bit tangled in the intersection between OPRHP and DEC who both seem to own aspects of trail use in NY. Not to mention the various private businesses who let DEC “managed” huge swaths of land to skoot taxes but still get to collect trail fees from private hunting clubs for use.
