@j-rider, road bikes typically do fine. I ride a bike with 28mm tires on it often, and that’s no problem. My friend rides the trail with 23mm tires, and it works.
As Timon said, the trail can be soft after rain (or snow), and narrow tires tend to cut into the surface, not only making it hard to maintain momentum, but creating ruts that will eventually dry out and create a bumpy surface. So that situation should be avoided if possible.