I definitely second/third going out on an experienced hunter for your first few times. Hunting is unlike most other horse activities and you will need to understand what is happening so as to help your own horse when he goes out for the first time. It is really helpful to have an experienced nanny ride with you, so you can ask all your questions and have informed responses as you go along. But: WARNING hunting is highly addictive and it could change your life!
There is lots of good sense about introducing your horse but, I’m in the UK and probably a bit more seat-of-the-pants about hunting. So, if your horse is in a busy barn with dogs and chickens and cats and lots of horse movements, if you show and he sees crowds and vehicles and tents and PA speakers, if your horse is generally a good character with sound training then he should manage. Even the hounds shouldn’t be an issue, particularly as your job is to keep your horse away from hounds. This is where your previous experience will help your horse though: if you don’t jump at hounds appearing out of the bushes then he won’t be so concerned. If you are out with horses from the same barn it is quite likely your novice will fix himself beside a stable friend and stay in that safe place.
As much as possible, take it easy and don’t overface him. If he deals with a situation, carry on, but if he shows any sign of over excitment, stress, tiredness etc then take him home so that the experience is only good. You can build gradually. There is always another day.
An alternative is to ask one of your experienced barn-mates ride him the first few times.
I took a riding school pony out once. He was used in beginners lessons, W/T/C in the arena, and some hacking with all kinds of riders. I doubt he had ever been hunting but he proved to be wonderful, really interested, polite, careful of other horses, completely unfazed by hounds and sounds. He was also fit enough, as a Welsh D, to keep up with TBs until he told me after a couple of hours that he’d had enough. I was really impressed and very proud of him.