It depends
Here is a thread where some of this is discussed.
http://www.chronicleforums.com/Forum/showthread.php?t=184127
I would say it varies from rider to rider and hunt to hunt.
Basically soundness and a good mind are #1 and #2.
Past that there are personal preferences and terrain and hunt style differences that may dictate one type of horse or breed over another.
Also depends if it is to go in the field or whip.
Many people (especially men) like them big. Personally I prefer a smaller one I can get on and off of. That being said my last three have been 16H which is larger than I prefer. I have one I’m bringing along that is 15.1 as a five year old. If she doesn’t grow much more she’ll be perfect.
You will see all varieties of horses (breed, color, size) in the field. They have to be sound with a mind that can deal with going alone or in a group. They have to be able to pony another horse and deal with hounds under their feet.
They have to be quick enough to miss a hole and stay on their feet in deep muddy or icy footing.
They don’t have to be as brave of a jumper as an event horse unless they are a whip horse or a Master’s horse. Usually there will be horse in front of them and a stop is rare.