The main benefit I see to hot mashes in winter is to get water and salt, which will get them to drink more water, into them. I had a mare who was such a Princess that if the water got too cold, she would refuse to drink. She also got impacted and lost a foal as a result of that, so I'm very careful to use tank heaters outside and heated buckets inside the barn. To make sure they drink enough, they get a little soaked beet pulp with salt added to their nightly feed and in winter I make it with hot, steaming water. By the time I get it out to the feed barn and into their feed it's cool enough to eat. They seem to really relish it at dinner time. So while I don't think it warms them, I think it does "go down easy" because it's warm and it gets water into them. Same thing with any other mash in winter, it gets water into them which will help keep their guts moving.
When I fed Alfalfa, in CA & AZ can't use local alfalfa here, I would make a bran mash a couple times a week and put a little vegetable oil and carrots & apples in it. I was feeding 10 horses at a time on it, so I'd put a couple of pounds of the bran and soak it down until it was oatmeal consistency and feed a little to every one. If I didn't think it was enough I added more to make the amount I wanted to feed.
It wasn't a real scientific process, and we didn't give a lot to any one horse. The only way you can be real precise is if you, 1 test every batch of alfalfa for its CA:P ratio, 2 weigh the alfalfa precisely each time and then figure out how much P is in each bag of bran. The idea is to not overload them with bran, but most alfalfa is pretty high in CA so, you bring in some bran to even things out. You know that ideally you want 2:1 CA:P, so just eyeball it and give a reasonable amount. Horsemen have been feeding bran for years with no ill effects, it just has to be in moderation.