Had the same problem this year with all the rain and snow, we walking out of our boots. I got a tri-axle load of what they call "Flume" in this area, it is limestone that is ery small like flakes/chips. We put it about 8 inches deep in three stalls that were constantly mucky (new stalls this past year) and then placed the 3/4" stall mats on top after compacting with a compactor. It has been almost a month of more rain and snow and no problems, almost like concrete. In front of the barn same issue as you are having, sun (when it is ever out) does not get to that area. It was so muddy walking and bringing in the horses and was miserable. I come out from the barn barn about 8 feet and went from one end to the other putting down the flume and compacting it. I did not dig out and for a few days there were soft spots from the muck under the flume, but now even with the bad weather it has really packed down to an almost concrete state, but is still not uncomfortable for the horses to walk on. I use a hand compactor for any spots the horses hoofs dig in and now that is happening very rarely. It costs about 9.00 bucks a ton here and so for about $400 bucks problem solved, we can now go out to the barn without needing to put on the mud boots.