Unfortunately horses don't wheelspin when they get stuck so they don't really cut up the ground as much as a 4x4 in certain conditions, they don't make deep ruts and they don't run on petrol or diesel, also, you don't get horses going off piste and causing damage where they shouldn't, or at least you-tube isn't full of horse riders going crazy on bridleways and byways. Equestrian activities are preferred to recreational 4x4 use (although horses are actually more dangerous) and so we will lose every time and the fact horses don't wheelspin gives people the excuse to shut lanes to us. That's just my opinion though.
Like I've said many times before, if I want to get stuck / muddy, then I'll go to a Pay & Play site. If I want to enjoy a nice quiet drive, enjoying the countryside, then I'll go laning, (and usually by myself or one or two others).
It's a reasonably affulant and rural area where I grew up and where I now find myself living again, so plenty of posh totty who are into their horses, many of whom I have known since childhood, (and my wife is mates with a lot of them).
There aint a single one of them who would even consider for one second not using a lane on horseback if that lane was already in poor condition or muddy and flooded.
I also do a lot of cycling, so I see the damage to bridleways as well as unpaved roads. And round here a lot of the earth is very clayey, which only makes matters worse.
Those on here who 'off road' in cars as well as horses may well be a lot more considerate than those who just ride horses. Maybe folk in other parts of the country are a lot more considerate too. But in my experiance, horses do just as much damage to muddy and flooded lanes as vehicles do.
Basicly, my long winded point is that if a lane is going to be closed to motor vehicles then I think that it should be closed to horse riders as well.