I don't believe in souls at all in the mystical sense. When I speak of souls, I refer to 1) a capability of being conscious that one is capable of death, 2) a capability of compassion, 3) a capability of understanding such things as right and wrong, 4) a capability of mourning for one who is dead or dying, and all of the other things that humans tend to think seperate them from most animals. All of these things are important because they are recognitions of the concept that we or another creature are something other than the flesh and bone that we are all composed of. Drawing an intellectual line between the state of being living and the state of being dead, for example, is a recognition that life is a special state of matter. As another example, compassion is a feeling that recognizes the suffering of another as something more important than how it effects that person's behavior or usefulness, something more personal.
Yes, to me, certain animals have souls. The whole reason that so many people believe in souls in the mystical sense is that we consider the life of something that we feel has a soul something beyond the condition of its body. Next time you see a horse playing in a field, watch it closely. Ask yourself if you can feel the wind whipping over your body as it runs, grass rubbing against your back as it rolls upon the ground. You can't sense that in a small rodent, an insect, or a reptile. You get the feeling that it has an awareness, a mind, a soul, even more so if you spend any amount of time in the company of one. I don't know how many of the multifarious aspects of what I would consider a "soul" a horse really has, but I'm bountifully certain that it has enough of them to seperate them from most other creatures, enough of them that, if I were personally attatched to one, I would mourn it if it were to die.
It's really too complex to be reduced to a black and white distinction. The mind and body are a gestalt of many parts of a greater whole. Functioning alone, the hippocampus, neocortex, and all the other parts of our brain would not be equivalent to a mind or, if you will, soul. In functioning together, they spawn something that is an existence unto itself, something that is no more mere flesh and bone than a car is a haphazard pile of engine parts or a beautiful song is mere noise. We are the product, the composition. We could, over time, replace every single part of ourselves with a clever machine that does the same thing and is subject to the same faults, and we would be every bit the same person as we will be after the seven to ten years it takes to replace every single cell in our body. This would make us wholly artificial, though, androids. To you believers in mystical notions of a soul, would we still have a soul then?
My point is that I don't think that a somewhat higher rate of encephalization in the neocortex distinguishes us so much from similar animals that we should consider ourselves entirely apart from them. We have a special sort of kinship with them, and they should have at least so much respect that we would welcome their company in an afterlife.