I don’t think the Caisson Horses are a particular breed - probably matched more for color than anything else. They seem to be a mix of various saddle horses with some draft blood. Just looking at their photos, seems like they have a lot of Morgan types (stocky but not tall). Unless all the riders are fairly small men, those are not your big draft or hunter types.
They are a mixed bag of breeds. Lovely animals and pampered to the hilt. My 10 y/o GD bonded with one in particular when we visited in April.....we couldn’t *drag* her out of the stable. ;)