@Philphed Check out the following links (they offer day trips, multi day trips and backcountry camps):
http://wildguru.com/en/tour-s_en/freeride_en/
http://www.freeride.ge/
I'm going there most likely around the last week of February and first week of March to hopefully get the best of some freeriding from the resort as well as good conditions for a couple of days in the backcountry around either Khorisar or Chaukhi.