Disclaimer- not a vet, or an expert on stem cell research. What did your vet say?
The whole point of stem cells is that they can turn into any type of cell (so you want them to turn into something specific in the body), and they're your own cells so the body doesn't reject them. The difficulties are getting them to the right place and getting them to turn into the right type of tissue, rather than a tumor. These issues haven't really been solved yet for most diseases.
I don't see how sheep stem cells would do anything- they would be foreign cells and the body would attack them. If we could use stem cells from other species interchangeably there wouldn't be the controversy over stem cell research in the first place.
From what I've read there's some evidence that you can use them to regenerate bone or get stem cells to turn into cartilage for osteoarthritis- but that cartilage will sometimes harden and exacerbate the original problem. Because the joint is already diseased, stem cells may sometimes form growths in and around this joint that may make things worse. At the moment it's pre-clinical (i.e. not shown to be effective enough to use normally outside studies). It may or may not work, it seems plausible that it will but we're not at the stage that we can say it does or doesn't.
"You can tell a lot about a purported stem cell therapy by how the “stem cells” are isolated and administered. If the physician doing the therapy can’t tell you what specific kind of stem cells he’s using, give a good technical description of how they are isolated and purified, show preclinical evidence demonstrating that they are, in fact, stem cells, and describe how he is going to target them to the correct area, then chances are good that the therapy is dubious." -David Gorski, oncologist.
This resource is for humans but has good info on this.
This article covers a number of different treatments for arthritis in animals, stem cells is no. 7 and has links to other articles on this topic, some reviewing the research in this area.