Horses also sweat. We don't seem to be too bothered by it (although I cannot claim to know what a sweaty horse smells like).

Also, cats and dogs do sweat a little, mostly through their paws.

Fun fact: part of the scary-effective logistics of the mongols was curing fresh meat into jerky using horse sweat during the ride.

You ever smell a dog after she's been playing hard in the sun for a half hour? It doesn't last that long, but they can get a bit fragrant.

I have known some dogs that drool more than any person can sweat.