Hound Excercise is not a time to school green horses or accustom them to hounds; it's a time to school hounds. Going out on hound excercise on foot yourself to learn about hounds and hound work is an excellent idea, going out on hound excercise on a horse new to hunting should be discussed thoroughly with the Huntsman and the Master, (if they're not the same person.) before doing so.
Not all fences have gates and 'go around' options; it depends on the hunt, the country that they're hunting and the preferences of the landowner. We had a certain piece of land that had panels, but unusable gates. The landowner didn't want to risk riders leaving gates open, so if you jumped into that territory, you had better plan on continuing jumping until you got out. Tended to thin the field out considerably when we went in there.
If you're new, plan on starting at the back of the second flight and reserve the option to drop back to the hilltoppers if the going is too fast or your horse too hot.
In the East, cubbing is in the fall. The original meaning of cubbing was hunting designed to scatter that year's cubs to new territory to ensure a good supply of foxes. Fall is the time the cubs are old enough to strike out on their own.
It is also the time new hounds are entered. Cubbing has a less formal dress code, usually "ratcatcher", and is usually less fast and less strenuous. The etiquette is the same as regular season.
Do not take your horse out unless you're 1.) sure you can control him in a group at all paces. (This is not a skill most people practice, and it's a shame.) and 2.) you're reasonably certain that he will tolerate being around the hounds. If he doesn't like the barn dogs, don't take him out until you've done a lot of work desensitizing. Hounds have the right of way in all situations out hunting, and the most grievious offense possible is kicking a hound.