Haven't been there with the bloodhounds but know the park and the area from hunting. I found these few pics on their archive. I would think you'd be in pretty muddy going, jumping some of the bigger XC jumps they have, but I do think there are ways around any you don't fancy tackling. I'd suggest ringing the Coahkham and asking what you are in for, they are very helpful. May see you there if I get brave enough by then!
Hiya, I've done the Brightling meet with the Coakham, its a really lovely day with lots of jumping, all hedges as far as I can remember had gaps near by (and that huge one certainly did) - there were some fairly meaty rails that you had to jump (there was a footpath stile or similar at the beginning of a line that caused problems for some) and quite a few ditches as well, lovely hunting country, well worth the effort from memory have fun xx
If you come out with the Coakham a good guide is you need to be able to jump 2'9" post and rail confidently, there is always ways round hedges but sometimes boundary fences are non negotiable. The going can be heavy at Brightling it is clay so you will need a reasonably fit horse as it can be a longish day.