We no longer have any pets, but when we did, they were always added. In fact, our dog, Lady, used to send her own cards to other pets of her acquaintance. Sometimes with an added gift.
Dog, cat, budgie, hamster, it didn't matter, everyone got a mention. Surely this is commonplace.
However, a rather large gentleman, with a full beard, suggested I was a nut. He was my boss at the time, so I didn't question his accusation.
Admit it, you do it too.