More or less signs of "el raton" a rat. Well at least you can see the route they are running, smart little rodents too, some traps they may sidestep for awhile. I would eliminate all food sources, but we all know how horses eat grains and pellets, sprinkling the bedding, gathering most but not all back up, amazing how they can pick through things.
I would move the horse and use a mechanical trap, with something they really like, possibly grind up some cashews, (rats love those) and mix with some peanut butter to make it stick. I would place traps along their routes. These rodents have extra sensitive noses, they seem to pick up on things very easily by scent.
I hate using poisons, but like many horse farms, rats show up at times, we've rarely if at all ever had them around, but just like your stall, you can see in the shavings where they make a hole, just under the bottom board, I did use poison bait, which I do not like using at all. I placed it out of the horses reach, more towards the exterior of the wall, some outside. It worked and rid the place of them at the first signs they were around, so they did not get established. We have to make sure that the feed room is cleaned properly, and around the stalls as much as can be done. These were some large ones too, brown, you would find them staggering around, young too.
I prefer a mechanical trap, because I can see what I have, no dead carcasses in walls reeking. No poison to worry about, as well as in dead carcasses disposed of, I like to feed em to the crows. We have one good barn cat, he's lined up 9 mice in a row, thats his record at least, but the size of the rats, no way he would attempt it, to be honest I never saw any that size in all the years I worked in NYC, including ones I have seen in subways.
