I think Phaedrus hit the main point. The real issue seems to have been that the conditions were so severe that SAR teams had difficulty even getting into the area.

Modern 406 beacons provide location data both by transmitting GPS coordinates and by Doppler shift. As J_V_A notes above, the GPS coordinates are truncated to an accuracy of 100 meters or so. Doppler shift alone gives a location to about 2 km.

In this case there isn't enough info to know why ".......a lot of the coordinates that we received over the night were all over the place within a mile circumference". It could be the subject was still moving around, desperately seeking shelter. Or perhaps buried under snow where the GPS couldn't get a good fix, but the satellites could still get a Doppler fix on the 5 watt 406 signal. I doubt the cold or weather conditions had much effect on the GPS chip, in Alaska folks regularly use GPS in conditions at least as severe.