This dog says he does.
Do you think our dogs want to sleep in bed with us because they are scared or because they want to cuddle with us?
According, to this article in Psychology Today Do Dogs Dream they most definitely do.
Our dogs, cats and most other mammals do have nightmares. We will never know what they are dreaming about. Maybe my dog dreams about the coyotes in the woods behind my house in Arvada, Co. But regardless of what he dreams he is welcome to crawl into bed with me.