Requirement 9.b.2 of the Camping merit badge offers this option:
“Backpack, snowshoe, or cross-country ski for at least 4 miles.”
Equestrian trails allow for fun backpacking adventures. One option is the James A. Reed Wildlife Area in Lee’s Summit with a youth camping area and an equestrian trail that passes several small lakes–it truly feels like a wilderness area.
One option: start at Access point 24 and take the white trail to Jack Rabbit Bend (1.47 miles), continue on the Orange trail to Crow’s Creek campground (2.20 + 0.42 miles), and you will have traveled nearly 4.5 miles by the time you get to the undeveloped campsite section, Loop D, in Crow’s Creek campground, which requires a 2-night minimum reservation ($36 for up to 10 people).