No. According to Idaho Administrative Code:
Dogs may be used to hunt or pursue :
01. Upland Game Animals, Upland Game Birds, and Migratory Game Birds. To train on or hunt
upland game animals, game birds, and migratory game birds.
Cottontail rabbits and snowshoe hares are considered upland game animals.
A hound hunter permit is only required for the following:
01. Use of Hound Hunter Permits.
a. The following persons must have a valid Hound Hunter Permit in possession when dogs are being
used to hunt or pursue black bear, mountain lion, bobcat, fox, and raccoon:
i. Anyone who owns pursuit dogs.
ii. Anyone having control of dogs owned by another person.