Lapaige,
You can still have pets in your active household, even if you have pets and horses turned off in the Game Options - Demographics Options tab, and Stray Animal turned off via Nraas Register
Stray Animal Control - Set Stray Animals to Zero 0
Selected Sim > City Hall > Nraas > Register > Animal Control - Set each to 0
This way you can still play with pets in your household, but not have a town full of pets if you don't want. lol
Awwww. I have pets turned off but I might have to reconsider.