This is a good idea, although pricey depending on the area and the arrangement you can work out. Sometimes people with elderly horses look for beginner riders just to get their horse some attenion and a little exercise. I know plenty of people who would let someone (willing to learn) do this for free or a small monhly fee.If you had the money a lease of a horse at a reputable riding facility would be more sensible than a dog. Physical activity, other people doing that, lessons and the horse is not "yours" and there are stable hands or barn owner to deal with poop.. and the horse can be turned back at any time.
If you are in an area with a good number of barns around you, you could call around asking if they would exchange riding time/lessons for help around the barn. Then she could spend time with horses doing chores (great form of exercise around animals) and even get some lessons for her work.
I second the idea of getting rats. They are basically like little mini dogs, and she could keep them in her room so you'd never really have to see them. I had them for several years and they are fantastic pets. There are even rat rescues and you can adopt/foster adult rats for a much shorter time commitment.
I don't recommend you get a dog.