There is no formalized national "polar bear" award or anything else like this for sleeping/surviving in ridiculously cold temperatures overnight. (nevermind the many various stock patches, even available from National on occasion)
However ...
There is a national training program for cold wheather camping, called OKPIK (pronounced ook'-pik -- translates as "snowy owl"). You can learn more about it from
http://www.ntier.org/okpik.htmlThe program started from the National Cold-Weather Camping Development Center located at the Northern Tier High Adventure Base at Ely, Minnesota. The program is now being rolled out in other councils. (Northeast Illinois Council has conducted a few courses now).
If you take the program at Northern Tier, there is a large Snowy Owl emblem for your red jacket (in the fashion of the Philmont Bull or the Florida Sea Base pink conch shell or the Northern Tier loon from their summer program). Other councils have developed their own recognition (our council uses clear plastic cubic beads on a white rope ... "ice cubes" worn in the fashion of woodbadge beads)