Have you checked the obvious.... something stuck in the driveshaft(s), wheels, brakes etc.? I've beat my 04 Rubi like a rented mule and it may have various issues, but no clicking when backing up except that time when the Honda was trying to blow it's horn 'cuz it was stuck under the back bumper and only the horn relay worked anymore...
Does it do it when on stands? Do you feel any "clicking" when rotating the wheels by hand? Does it only do it when reversing while turning, or straight as well? Is it a metallic or plastic click? Is your park brake completely off, or is it partly held on with packed snow holding pressure on the cables? Could it be your park brake adjusting, ie: does it click only once when beginning to reverse, or does it keep clicking as you keep reversing?
I'd probably go visit Lemon-Aid Jay if I couldn't figure it out myself.