The problem with *both* bikes and horses (and hikers) is simple:

1) Overuse wrecks things - and requires people to rehabilitate or mitigate:
- muddy horse poopy trails
- massive trail braids in wet areas from hikers
- deep ruts and shredage from bikers

I have seen *all* of the above in my usual haunts.

2) Jerks, Slobs, and Buttheads ruin it for everyone.

While yes, I've had a bad experience with a biker, I'm sorry there's no shortage of boneheaded hikers either. All the above can be morons on the trail, leave garbage around, etc.

Personally, while I won't go as far as allowing motorized vehicles, I don't have a big issue with wheels, as long as rules are there and respected to keep everyone safe. in that respect I'd rather be inclusive on trails rather than exclusive. I'm betting we'd have more responsible bikers if they were exposed to having to share the world more too.