I must say, this is a funny yet valid question. To answer your question straight away, yes, animals snore. Snoring isn't something limited to humans only. Snoring is something which occurs when air can't freely flow through your nose and throat and as such causes the tissue in them to vibrate and produce a weird sound that nobody likes to hear. So basically, if air isn't flowing freely and properly in a throat, be it a human or animal throat, the creature is bound to snore. That's why fat people are bound to be snorers. Also if you sleep in a position where your throat is compressed, you're bound to snore too. Other people that snore are people who have nasal blocks or constrictions.
Now for animals, it's safe to say that all the above listed things can happen to them too. An animal can be fat, sleep awkwardly or have nasal blockages and so an animal can snore.