I have seen most of my animals dream; the kitties, the dog AND my horse!
As a matter of fact, my older horse was laying down and twitching, I dropped the wheelbarrow, hollered at him and ran towards him. When I reached the poles of his corral and made them rattle as I tried to quickly crawl through, he startled awake and gave me SUCH a disgusted look for disturbing his sleep...
I'll tell you though, I almost had a heart attack and was already crying, thinking he was having seizures.
The dog would dream and I've seen the kitties dream. Shadow is the only kitty I have that snores. Unless kitty has trouble breathing while awake, I don't think it is anything to worry about.
They sure keep us guessing and worried, don't they?