Not necessarily. For most recreational mountain bike trails I'm familiar with, access is at the landowner's discretion. Famously, a few years ago, landowners in East Burke revoked access on what had been some of the most popular trails in the state.

On the other hand, I know of some properties that the state sold to timber companies where public hiking access was a condition of the sale. Not sure what sort of legal process would need to happen to get that changed.

And then there are town highways and legal trails. These are public rights of way found on the town highway map that pass through private parcels. If a new landowner wanted to prevent access, they'd need to go through the town selectboard who would bring it to a vote. This seems to happen regularly.