The big belly can be a sign that the mare is having trouble digesting the hay so it stays in her digestive system longer, which could be due to a problem with her or the fact that the hay is not good quality. It can look good and clean but still not have much nutrient value. You can get this checked through your local ag extension agent or university. Also, if she is ribby, she needs more fat in her diet, either through additives such as oil or pellets/nuggets, or by getting a feed with higher fat value. You can find good feeds which have higher fat (for the weight issue) and protein (for the topline) that are also lower in sugar and starch (higher sugar or starch, given as NSC value, will create the excess energy you don’t want for your daughter’s horse). I would suggest looking at whatever feed brands are easy to get in your area, and then research their feed types and talk to their feed rep or nutritionist for your area. Four lbs of feed a day in the winter especially is not much for a big horse that needs weight, so make sure you are feeding amounts according to the recommendations on the feed tag. Ulcers could be an issue causing the mare to eat slowly, or she may just not like the feed. Your vet should eliminate any health issues, such as tooth problems, ulcers, or wormy issues thru fecal exam. We used ranitidine prescribed by vet on several horses suspected of having ulcers last year and it really helped their attitudes and comfort.
Hope these suggestions help. Best wishes in getting your horse healthy for your daughter.