I made up a house rule on the spot today that I want to share. When the alligator struck, I had the horses make Fright Checks, which is common. Both wound up fleeing: Ash's riding horse right away, and the pony after a few seconds. After the fight, to round them up, I had Ash make an Animal Handling (Equines) roll. He missed by 6, so I ruled that he spent the next three hours looking for the horses.
So, here's the rule: if your mounts or pet dogs run away in a wide-open wilderness (not a dungeon), make the appropriate Animal Handling roll. Apply the penalty from the Speed/Range table for long range, reading "yards" as "animals." Thus, a lone horse gets a +2 bonus, the two horses got no bonus or penalty, and three horses gets a -1 penalty, and so on. If you succeed, you get them back with little fuss. If you don't, you get them back after a half-hour for every point by which you missed the roll.
This not only speeds play, as I don't want to game out every time the horses bolt and run (which is pretty much all the time, as neither is combat-trained), but encourages folks to spend points on seemingly useless skills like Animal Handling.