If you ask me, Deerfield would be a winner among the three - by a slim margin. It appears the most balanced of all, lacking nothing, including the intangible “happiness” factor. It looks least trying, coerced or contrived because it already has everything in abundance. Congratulations!
Hotchkiss is both rigorous and beautiful, but quite isolated on mountain top. Summer is gorgeous but your time there would involve more winter than summer. If you love snow, great.
These two are really America’s best in terms of facilities, in my opinion. They are Ivy college level.
As for Loomis, I do not know much other than (1) it is one of the up-and-comimg schools, super-hot among applicants these days, and (2) one of my friends was so impressed with his son’s “transformation” there that he started making large donations purely out of his own will.