Bran mashes will not protect your horse's digestive health. In fact, rice bran or wheat bran confer few, if any, health benefits for horses and carry some risks.
Bran is believed to have a laxative effect in people, but to get the same effect in a horse, you'd have to feed huge amounts of it-more than he could eat. Some horses do produce softer stools the day after eating bran, but this probably reflects bran's tendency to irritate the lining of equine intestines. If fed daily over a long period of time, bran may actually contribute to the formation of enteroliths.
But the bigger danger of feeding too much bran to horses lies in what it can do to the dietary calcium-phosphorus ratio. The two most abundant bodily minerals, calcium and phosphorus work together to build sound bones and assist muscle function. To do so, however, they must be absorbed in appropriate proportions by the body, which means that when a horse ingests phosphorus, he must also ingest an equal or, preferably, slightly greater amount of calcium.
If there's not enough calcium to match the phosphorus in a bran-fed horse's daily feed, his body will pull extra calcium from his bones in order to balance the excess phosphorus in his gut. If a horse gets too much phosphorus over too long a period, his body will take so much calcium from the bones that it weakens the skeleton and leads to bone disorders such as "big head." Grass hays such as timothy and orchardgrass contain the exact ratio of calcium to phosphorus that horses need; wheat bran and rice bran contain about 10 times too much phosphorus, on a per pound basis.
That said, an occasional hot bran mash won't harm your horse, and he'll likely relish the treat. Likewise, small amounts of bran can be incorporated into the daily diet, as long as the horse gets enough calcium from his other food sources.