A lot of chicken owners I know use it for bedding in the hen house. Apparently, it absorbs the heck out of some odours. It also creates some really nice compost. The only reason I haven't tried it yet is the limited supply. It's not a "renewable resource".
I have always been told that peat moss is a great solution for horses who struggle with allergies or dust inhalation.
Here's a good article from HorseSport that might interest you though.
It compares different bedding options: (including Peat Moss)
My horse has been in peat now for nearly two years where I board and it does seem great. For a while we had several horses with foot problems and people were wondering if it could be the peat.
But over-all feet issues seem to be better for a while now. I suspect if the peat is contributing to foot problems it's not being kept clean enough. Chore duties were adjusted to lessen any wet spots. One out of three people cleaning was too lax about digging out the wet spot but cleaned out the pooh pretty good. At this point with my limited experience, I'd say the peat is great if maintained properly. And ours seems good now.