It depends on the quantity. Adding 1/2lb of bran to a meal isn’t going to cause any upset to any but the most delicate GIs.
People give horses an apple out of the blue all the time 
Feeding them bran mashes is a really bad idea- causes all kinds of stomach upset. Not sure who came up with the idea of mashes, but it’s not good for them.
Again, it depends on what you define as “bran mash”. Replacing a regular meal with, say, 1/2lb bran, a cut up apple and carrot, and adding some water, isn’t going to hurt him. But some take “bran mash” to mean replacing the regular meal with 2-3lb of bran, a few apples, 1/2lb of carrots, a cup or 2 of molasses, etc, and that could very easily cause a bit of trouble
So if you don’t normally feed them soupy meals, don’t suddenly start.
Don’t suddenly add water - which they already consume - to a meal?
There’s no harm in making a meal into a soup, or wrong out sponge, or wherever in between. It’s no different from the horse eating a bite or 2, then taking a drink, and repeating