For the mopst part, my dogs are kept inside or kenneled while I mow since, years ago, I had an Australian Shepherd that tried to herd the running mowers. *sigh*
I do have a poodle now that I allow to ride the lawn tractor with me (without the blades running) because he likes to think he's a farm dog.
One trip around the yard and he prances and grins all day. Silly guy.