I've hunted 4 times with different hunts throughout Maryland. It's SO much fun! And they don't kill the fox in the US, we just chase it til it goes to ground (in it's hole). They are killed in England because they are considered vermin, however.
The first time I went my horse was a little unsure of the hounds, but he got used to them very quickly. He was also 5 his first time out and when we were standing at checks he was very impatient (and some hounds ran off to east-jesus so we were standing for a LONG time while they were gathered back up), but by the end he was snoozing in the shade.
If your horse gets a little fresh out in groups I would stick a martingale on her - I use a running, but most hunt horses go in standings.. it might give you a little more control, but worse-case senario, it's a great "oh crap! Strap" to hang on to if needed ;)