Can we put pets in storage?
If we put pets in storage, do we lose them?
You can stick pets in storage and zoo animals too. You do not lose them. I've had to stick many of my zoo animals in storage because I got way more animals than I had room for and my expansion was four days away!
You will notice that pets you win through goals will be put in your storage. So, perfectly fine to put pets there.
The only issue is that you can't crossbreed them if they are in storage.
If you try to buy a pet from the market and you have it stuffed in storage, it will ask you to place the one from storage.