I can hot walk her for thirty minutes and let her graze on the grass in the outside paddock, she'll hold it until she gets back inside and can use the nice clean shavings I put in when I was saddling her up in the crossties.
When I was a teenager I broke and trained a horse named Honda (my friends' dad sold his motorcycle to buy him) who had the same idiosyncracy. Basically they built a little enclosure (not really big enough for a paddock, about 30 feet square) behind his stall, and put in a back door which they left open. He would wander out and down to the very back of the enclosure to do ALL his business in one corner. We just kept dumping sawdust back there! He never "went" in his stall, not once that I can remember.
Their dad built a porch roof over the back of Honda's stall so that rain &c. wouldn't come in the open door. It worked out quite nicely. Honda used to stand in the doorway to enjoy the breeze in the summer.
He was a nice old boy, a dark bay grade gelding about 15.3 with a good deal of Quarter Horse in him. Kind of shambling gaits (and I didn't know enough dressage to tighten him up) but he was good natured and perfectly willing to jump for me, although he did tend to drop his forelegs into his fences. I'm sure he's on the green fields of Heaven by now.