Hunting cougar with archery in Idaho is an excellent option. Most shots are 30 yards or less and a good medium weight arrow tipped with a 100 grain broadhead is sufficient.
Taking a mountain lion with a bow is not as slam dunk though, as it does present it’s share of challenges. Bows are typically cumbersome and on a long chase through the rugged Idaho mountains, they can become heavy and get hung up in the brush frequently. Also I’ve seen many times where ice and snow gathers on arrows during the trek and this can create some accuracy issues.
That being said, a pope and young cougar is fairly average in Idaho as most mature toms will reach the minimum requirements easily. Remember that Idaho does not allow mechanical broads so plan accordingly.