Riding a skinny horse?

To me, I think she would almost be too skinny to ride. Obviously there's a lack of topline, but in the closer photo without her blanket, I can see her ribs even with the winter coat--to me that means she's too skinny to be riding.

If you want to exercise her, you should try round penning/lunging her while you're getting her weight up.

If you choose to ride or drive a horse with in adequate conditioning you run the risk of causing spine alignment issues and front end issues. Judging from the photo and her age I would agree with 15 min tops to help build muscle. I would look at a good senior feed. Also a vitamin B injection will help motivate her metabolism so it operates at optimum.