There is a reason that your mare is fat- you're way overfeeding her!
Do you know her breed? Many ponies- especially shetlands and miniature horses (which, ofcourse, are technically not ponies, but are
very small and often cross bred to result in mixed ponies) are notorious for having finicky stomaches and for getting fat on air. Giving them rich or sugary feed such as pure alfalfa, sweet feeds, and additives such as oats, corn, etc can be detrimental to their health.
That being said, I honestly think that you need to take your pony mare off of everything that you're feeding her- save for the costal hay- and make some changes.
We have a horse farm with over twenty minis and ponies of all life stages and occupations. Show, breeding, companion, therapy, you name it- and we feed very little grain. Most of them are on free choice 2/3 timothy 1/3 alfalfa hay, a few are rationed a flake and a half to two flakes daily. Those that need supplimented with feed (mostly our show and breeders) are given either a Purina Miniature Horse and Pony feed or SafeChoice Special Care Horse Feed from Nutrena. I personally prefer Nutrena, but you have to find what works best for your mare.
Once you select a feed (if she needs one at all- MANY ponies are VERY healthy on just quality hay), you need to calculate just how much to give your mare. The crimped oats are not good for her, and while rice bran is not bad- it is not for easy keepers. My guess is that she doesn't need the alfalfa pellets either. I would start her on 2 cups of a well balanced feed twice daily with nothing else except hay, and see how she does. We have a shetland pony gelding who is 42 inches like she is and, I admit- rather overweight, and we only feed him that amount dispite the fact that he is ridden for therapy 3 times a week. My miniature horse mare eats even less than that- she is on free choice hay normally and is at a perfect weight usually. She just foaled a month ago though and is now on the Nutrena feed- 1/2 a scoop twice a day- and she looks phenominal. They really just don't need much!
Our oh-so-skinny shetland pony gelding ;)