The damage comment is ridiculous, the damage caused to the ground in there is caused by the rangers in their land rovers.
My wife rarely rides her horse in there anymore as the ruts they have left could cause serious injury to a horse in canter. And she has received some very obnoxious comments from the small minded old giffers who think they police the place.
As for horse riiders behaving themselves, there's plenty who go in out of the allotted times (ridiculous idea!) and ignore the marked horse tracks.
I ride bikes in there, but only out of hours just to reduce the grief.
Swithy woods is fair game anytime. Just be polite, smile and be courteous.
Personally I think bikers and horse riders should join forces. The idea that horse riders want flat groomed wide tracks is dreamt up by some ignorant council access numpties. Riding narrow twisty trails on a horse is fun for them as well.
There's actually a fair bit of fun trails around here if you really start searching considering the location.
Also there's no way I'm getting in the car to go riding when it fancy a blast out at 9pm on an evening.