I have seen ATV trailers parked in the main parking lot before... whether they were allowed to or not is another story, but i have definitely seen them. I woukd still call before you make the trip out.
I'd call them. There is a large parking lot but i don't know if ATVs are allowed. Sorry I couldn't be of more help.
The primary ATV parking is at the end of Ray Road in Dunbarton, which is the backside of the state park.
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