Someone correct me if I am wrong, but I am not sure there are "sizes" to instant hot water heaters as they give an unending supply of hot water as you use it, I'm sure there must be some kind of difference that I am unaware of. The tank on the other hand requires more thought, how often are you going to bathe the horses in the winter? How many do you need to bathe in succession, is a washing machine involved, old ones can use 20 gallons or more per wash. I have also been thinking this question over as we are building a barn. I have concluded 15ish gallons should be good, we only have one horse that ever goes anywhere with any regularity the other two just need GP and mud removal baths, other miscellaneous things so really only need enough hot water to give one bath at a time. Also not sure of the electric wiring requirements for an instant are they different from a tank? That may also be a consideration.
Yes, there are different size on demand hot water heaters. I have one for my master bath. I don't think I would want one in the barn. They use a lot of electric. I have a 10 gallon tank heater in the barn. I would probably go a little larger if I did it again.
10 gallon is too small for a horse bath. We really don't bath on the cold days. Lucky that cold days are usually only a few at a time here. It is enough to wet down horse and fill the bath bucket, usually warm by rinse time. We usually only use it during the winter and now for a horse eating hay cubes. During the summer it's usually unplugged.
We use a Toyotomi Oil Miser to provide hot water to our heated vet room. Works great and can run on B20 biodiesel. We also have another very small unit, but I don't remember what its called. Both work great at providing heat & hot water, even down to -30F. As far as heated waterers, we love our Nelson waterers.