I suspect some of the tags on public footpaths should be permissive and not yes (it is a right which can be withdrawn by the NT not one granted by law). I'm a bit out-of-the loop with what the current standards are for NT.

Years ago when Curly Carver was warden there were some issues about which paths horses could use (Broad Ride in the Thicket was one). I think I did map the broader rides on the part of the common near the cricket ground as bridleways. 

Either way being explicit about whether riders are permitted or not is definitely a good thing in an area with so many active riders.

Jerry aka SK53