IME it has been quite aggressively policed (wardened?) by the warden to keep people off anything narrow and twisty. There are some bridleways across, and at the eastern side in the woods there are a few more interesting bits, but the open bit is as above either boggy, or sandy, and for about 15 mins per year ‘goldilocks’ and just right.
My best experience was on a gravel ride, so actually perfectly happy slogging E->W along the sandy bridleway and warden prick came racing towards me at about 60mph from about a mile away, kicking up masses of dust and sand and scattering horses and children under his wheels as he approached (OK, poetic licence, but he was definitely ‘eroding’ stuff on his way) He roared up to me, pointed at a narrow path up towards the road and shouted ‘You can’t go up there!’
– I know, I wasn’t going to
– yes you were, I know you cyclists, you’re all the same
– But I wasn’t.
– ah, but you would if I wasn’t here!
– nope.
(and repeat over and over)
Sort of Minority Report, Bridleway edition.