I've always cleaned, wing attached, and placed the bird in a bag in refrigerator to cool overnight. If fridge is too small, like a hotel, then transfer bag into cooler (kept indoors) filled with ice. Process when home.
Fantastic in stir fry, fajitas, or my wife's favorite...tacos. Agree NEVER overcook the breast meat. Thighs and legs low, slow and moist bake...good eating.
Another strike out here, points for next year! Last prairie chicken I "got" in MN I saw hit a power line and break its neck during a deer drive in the old NW MN slug zones.
Used to be a fair number in central MN 40 years ago, shot a few every year pheasant hunting. Haven't seen a hun here since at least the early 1990's. Too damn bad...fun birds.