Beet Pulp works similar to the way Psyllium does, and my vet suggested increasing beet pulp for my mare when she was colicking. You can add a Psyllium supplement like Sand Clear to her diet to increase fiber and help things pass through easier. Anything high in fiber is good, and yes, she can and will gain weight on a hay only diet. Hay and grass are some of the best things for horses, and when provided with enough of it they can thrive perfectly fine. Get a good quality grass hay. Legume hays are also really good for them.
Good luck with everything! She's a pretty girl!