I ride my bike there all the time. Bikes don't tear up the trails near as much as the horses. Plus, all those new bridges and cross overs and plank trails through the bog are courtesy of the local mountain bikers.
If you see someone riding rudely or off the trails, please accept my apology on their behalf, 99% of mountain bikers are courteous, and very conscious of trail etiquette and know we'll be the first ones tossed off the trails.
(The 1000 pound hooved poop machines crowd seem to hold sway somehow)
Funny thing is, I see all the horse crap, but as much as I'm there, have never seen a horse on the trail. I guess they are there early in the morning / middle of the day while I'm at work.
At any rate, yeah, I suppose on average, individually, the bikes do less damage, but there are far more bikes on the trail than horses (I believe) based on my first statement of zero sightings of horses. With respect to the behavior of the bikers, I'd guess it at about 50/50 for those who are courteous and those that think they own the trail and that you should get out of their way. I had two blast by me the other day while they were on a down hill run and they obviously had no intention of slowing down. If I had not moved, it would have been a bad scene.