I do not have any of the 36 listed felonies. It has been 14 years since having any trouble and would like to hunt with my kids.
Provided you don't have a provision in any felony conviction that prevents you from owning or possessing a firearm; you've purchase a valid hunting license and tags;
and have taken an archery education class or qualify for an archery validation - then you can use your archery equipment during a rifle season to harvest a game animal.
IDFG Note 8/14/2014 4:15pm MST: Oops, we goofed. One does not need the archery validation to hunt with a bow during any weapon (rifle) season.
If you're interested, you can read Idaho Code Title 36, Chapter 409 (e) for archery restrictions. It states the hunt must be specifically designated as an archery hunt to need an archery permit.