it took me awhile, because there is nothing specific about a "muzzleloader" being possessed by a felon - so i needed to locate the definition of "firearm" and the ORS state the following definition under 166.210
3) "Firearm" means a weapon, by whatever name known, which is designed to expel a projectile by the action of powder and which is readily capable of use as a weapon."
given that definition, coupled with the fact that oregon also denies possession by a felon of any antique firearm - because of how it is defined - my opinion is you cannot hunt with the muzzleloader
but my research did reveal that if your rights to hunt have been restored, you can use a muzzleloader in the State of Washington - just an FYI since you are neighbors.
FYI - definition of antique firearm, which by Oregon law cannot be possessed by a felon, either -
1) "Antique firearm" means:
(a) Any firearm, including any firearm with a matchlock, flintlock, percussion cap or similar type of ignition system, manufactured in or before 1898; and
(b) Any replica of any firearm described in paragraph (a) of this subsection if the replica:
(A) Is not designed or redesigned for using rimfire or conventional centerfire fixed ammunition; or
(B) Uses rimfire or conventional centerfire fixed ammunition that is no longer manufactured in the United States and that is not readily available in the ordinary channels of commercial trade.