And believe me as a horse owner and rider- people have VERY different ideas about the nutrition and diet of horses. I would do your research and in the new barn I would print out a feeding schedule and make sure that whoever will be taking care of the feed adheres to your feeding schedule. I would do the following...
Hay- as many flakes as you think necessary. In my barn we throw hay many times a day and when the weather is cold we make sure the horses always have hay to eat.
Grains- We do morning and evening feedings 1 scoop out of a coffee can as you described before
Alfalfa cubes- get a big bucket of these and wet them down with warm water and pour about two table spoons of corn oil on top. you only feed this once a day.
Also make sure that you are exercising the horse as well to keep their metabolism up.
Oh and in case you were wondering I have two horses
And a TB is a Thoroughbred