For many of us, muzzleloader and black powder weapons were the reason we got into the hobby. I grew up with my father being really enamored by the process of shooting and maintaining black powder weapons and the sweet sulfur smell of burning black powder. The first pistol I ever shot was a black powder gun and almost all of the hunting I do is with primitive blackpowder weapons.
If you are already going to rendezvous and competing in the shooting contests and already a hunter, why not take it a step further and use your black powder rifle or fowler to go hunting? Despite persistent rumors to the contrary, black powder replica rifles are excellent for harvesting rabbits, dove, quail, deer, hogs, and anything else you can find in your local wood lot or hunting area. Elk, moose, and even brown and black bear have all been successfully harvested using "primitive" black powder weapons. The late, Val Forgett Sr - founder of Navy Arms Company - even managed to hunt all of the "big five" African game animals (Elephant, Rhino, Cape Buffalo, Leopard and Lion) with a muzzleloader.
In the spirit of the original rendezvous, most of the mountain man's year would be spent trapping, hunting, and in the small groups that would trap the rivers of the Rocky Mountains region. In this regard, the actual time spent at rendezvous was very minimal and the exception, rather than the rule.
Thus, it's completely within historical precedence to spend a good amount of your non-rendezvous time hunting and trapping. Hunting is a great time to work on your primitive gear in a realistic setting. You can see how your rifle, hunting pouch and powder horn work when you are moving in the woods on the trail of a deer or elk and the deer camp is a great place to introduce folks into primitive skills.
Sam Fadala's quintessential tome, The Complete Blackpowder Handbook, is a great place to start for more information, although in recent editions it has taken more of a focus on inline muzzleloading rifles which are not really in the spirit of buckskinning. If possible, see if you can track down an earlier copy at the used bookstore. It will save you money and include more info on the "sidelock" rifles that are the essence of the hobby.
Many states have a muzzleloading season where folks with muzzleloading firearms can get an extra two weeks or so of hunting before the general season begins. Sometimes this is grouped together with archery and sometimes they are separate times. It would be exhaustive to try and list out the rules and regulations for each state, but your state parks and wildlife/fish and game department will have all of the information on these seasons and when they occur.
Though they are usually open to all types of muzzleloading firearms, some states restrict the season down to type of ignition - flintlock/percussion - as well as the caliber of weapon you can use! Inline muzzleloaders are usually included into this list of acceptable weapons, but as mentioned above are not historically accurate, were invented in the late 20th century, and generally use ignition systems that are only marginally similar to original and replica black powder firearms.
I once stood transfixed on a hunting video in a Sportsman's Warehouse store where the would-be deer hunter took careful aim with his inline muzzleloading rifle after using a laser rangefinder, nylon/zytel cross sticks, and a scope - shot the deer and then exclaimed in joy about his first "black powder deer!"
I have no quarrel with anyone who hunts in an ethical manner, but in the traditional department inline muzzleloaders do leave something to be desired.
The true essence of the mountain man is trapping and trapping is legal with the proper licenses in most every state. Even up to the 20th century many folks would supplement their income and their living with the money earned from trapping. My wife's grandfather earned extra money in lean years by trapping and when he retired spent at least two weeks of every winter trapping to raise money for the mission trips his church would take.
In some agricultural areas, there are still bounties on trapping animals that would otherwise damage valuable crops.
The best way to get started into trapping is to find a mentor who can show you the right way to ethically trap and harvest animals. Because trapping is essentially "hunting" in absentia, it is also a valuable strategy for survival situations and is a great skill to know. Trappers are closer to the land then hunters as they have to be there day in and day out checking their traps, looking for sign, and really getting into how animals are moving about the woods.
Because traps can be dangerous and can unintentionally injure humans and other non-game animals it is essential to know what you are doing when trapping. There are quite a few great books out there, but nothing can substitute for finding someone who knows what they are doing who can help show you the ropes. Or the chains, as it were.
Make sure you know the rules and regulations of the area where you are hunting and trapping. Being in primitive garb and good intentions won't save you from a fine or possible jail time.