I have been on he same boat on you. Last year, Casey's stall was a muddy mess, and her pastures were wet. She did get some mild thrush, but we dealt with it.
Obviously, you can't really put concrete or gravel over the mud, and mats can get sucked into the mud, and they would just kinda slosh around over the mud.
What I would do is to get at least 3\4 inch thick plywood.
Take a shovel and try to shovel out as much as the mud as you can. It is a back breaking job, but it is worth it for your horse!
Then, get some gravel, preferably the big chunky stuff for gravel roads, and put a couple inches of that over the ground you have been cleared.
Put the plywood over that.
Add LOTS of shavings, and each day check the plywood.
Make sure you desentize your pony to stepping on plywood, first put it on the ground somewhere and practice have her go on it.