I usually take a cap 'n ball pistol with me deer hunting, either my Old Army or a '58 Remington. The main purpose for me is when tree stand hunting, being able to make that shot off of your strong side at close quarters, a shot that would be impossible to swing that long barrel flintlock around to make. I have done this for several years and the opportunity has never presented itself, but one of these years it will so I continue to carry one into the field. It will be a nice photograph when I do.
The point about the state laws is a good one. Where I live there are no restrictions on the size of muzzleloader you carry into the field, its power or the number of individual firearms you may possess while hunting. A lot of other states are not this liberal, you will want to check your local laws.