Ski mountaineering near Gudauri

I'm visiting Gudauri on February 18th to 26th and I would be interested in doing some ski mountaineering in the area. Is Mt. Kazbek too early in the season to attempt? Are all of the 4000ers in the area at least 2-day trip away (approach on day 1, summit following morning)?

I have extensive ski mountaineering experience, also twice from altitudes above 7000m. I will also bring all necessary equipment but private guides may offer their services.

Contact: http://www.gudauri.info/accommodation/hotels/gudaurihut/

Gia Apakidze
Director, Gudauri Hut.

Gia has a 12 year experience of heliski guiding in Gudauri. He is a master of sports in mountain climbing, a mountain guide and a member of the Georgian mountain rescue team. Gia is certified jointly by the International Federation of Mountain Guides Associations (Switzerland) and the Georgian State Mountain Guide School.

Prior to the 2011-12 season, Gia was the chief of the Service Ranger Gudauri.

And you can read it: http://wildguru.com/en/tour-s_en/freeride_en/programm_en/ (the distant spots).