mavka13 Sorry for the late reply; I haven't had time to answer posts for the last few days. NRaas Register allows you to control (or remove) the stray pets, wild horses, and deer and raccoons in the world, and keep them gone. I would highly recommend this, especially for wild horses, any time your sims are not actively interested in adopting the horses. Their routing is awful and they're difficult for the game engine or underpowered graphics chips to render. Combine that with the funky routing in Bridgeport, and it's a recipe for disaster.
The only mod I know of that disables pet adoption for inactive households is NRaas StoryProgression. You'd have to change the settings, and additionally, SP is something of a heavy mod. But you could also run it on the slowest setting, and slow down the cycles further, to limit its impact on the game. It wouldn't affect your main household at all on default settings.
Horses and long-haired dogs are harder to render than short-haired dogs and any cats, so you could also let that guide your decision making. And having a couple pets in your active household but keeping them out of inactive households, or severely limiting the population, will improve things somewhat even if it's not really a fix. So you could try to find a balance between performance and keeping the features you want.
I would also suggest picking and choosing where your sims have pets, or certain types of pets, for example maybe they only have a cat or two in Bridgeport but raise horses in Appaloosa Plains or Riverview. The more space the better. This isn't critical, just another way to help the game run better.
Finally, the Pets Need Less Space mod can help a lot in tighter spaces. It's newer and hasn't been tested nearly as much as other mods I recommend, but there aren't any problematic reports I've seen. I use it myself and have noticed no new issues, plus it shouldn't cause problems based on what it modifies.
https://modthesims.info/showthread.php?t=682926
