When you say trails, what do you mean? There are some mountain bike specific trails in my locale, but they tend to be relatively short. But when you mention that the trails span multiple counties, then it suggests what we have a lot of in Wisconsin -- wider paths that are covered in a very fine gravel or crushed limestone. Of course a lot depends on the specific condition of those trails, but my "fun" bike is an old road frame with relatively narrow tires and it handles those kinds of trails just fine. Since I anticipate more of this kind of riding, I'm planning on moving to wider tires.

For any two kinds of bikes, somebody will come up with a new kind of bike that's in between. I've seen so called "cyclocross" bikes that can accommodate wider tires for comfort on trails, but that wouldn't seem out of place on paved roads.

Now if you're talking about real mountain bike trails, those would not be too much fun on a road bike.