I've heard religious people say animals don't have souls, although I view the "soul" as the energy that is within us all, I believe this to be an untrue statement. I would think that we most likely run on the same energy just a different vessel. Was recently in a debate over this and made the points of; does a dog not dream, does it not show affection, does it not have a desire for treats? Ect.. Point being they share the same emotional reactions so I would believe if the "soul" is a real thing I would say animals have one too.
If you ever have a dog or any animal you will believe beyond the shadow of doubt that they have a soul.
My best love to dogs, cats and all animals.
I guess it depends on what you mean by "soul." "Soul" in the poetic sense, yes. In the sense that when they die they still exist and have experiences in another plane of existence, no. My animals have vibrant personalities and character, but I don't use the word "soul" to describe them.