The only lead that I can give you is south of Utica. Apparently it's called Charles Baker State Forest, I knew it as Brookfield State Forest. I guess Brookfield is just 1 section. There are over 130 miles of trails that from what I know are used a lot by horses, so I don't know how "rideable" the trails are. Here's a link, maybe give the local forest ranger a call and see what he has to say. The southern adirondacks aren't that far away I just don't know what is rideable close to Utica. I did a race not that far away called the black fly challenge and I know there are some mtn. bike trails in that area, just don't know if there are a few closer to Utica too.
http://www.dec.ny.gov/lands/8225.html
http://www.dec.ny.gov/lands/8225.html