It's not that I can't interact with the horses, it's only that I am missing a single interaction.
Are you missing the "pet horse" interaction?
I can "Rub Neck," "Feed Produce," "Let Sniff Hand,"--everything except "Pet." Which is actually relatively minor, except that there are wishes that pop up to "pet horse." They don't give many reward points, but if you've got a Sim who is an equestrian or animal lover, this wish is likely to show up a lot when there are horses nearby. And missing that interaction does also mean there's less you can do with horses in the game.
If you aren't you aren't, and it very well could just be a problem in my specific game. Only, similar to the inability to "chat with toddler," I don't think that I had this issue prior to Into the Future. But, I also hadn't been playing with horses the last few games--and had spent a lot of time in Bridgeport for a few games where there were no horses.
I've had this glitch occur in two separate games, one with CC, then after mods were added, and now in this completely clean, CC-free, store-content-free, mod-free new game in a totally different world. The first one was in Pleasantview, this one is in Moonlight Falls. I didn't want to test with any custom content, store content, etc. and so I won't be trying with Dragon Valley until I go back to my regular setup with mods. Pretty sure that the world isn't the issue here (and if it were, I'd still want to test it outside of store worlds due to the fact that most players probably don't have any of the store worlds).