My one arctic experience was on Denali more than thirty years ago.  Climbing the Muldrow glacier, I was good in plastic double boots (an REI purchase).but once we got to Advanced Base Camp at 14,000+ feet, we switched to military surplus mukluks which were nice and toasty in that relatively sedentary situation.  I was a volunteer for Denali NP, on the June patrol.  We were cleared for a summit attempt if the opportunity arose, but our primary mission was to support the climbing effort and deal with emergencies, which were numerous.  Our summit attempt was thwarted because we were dealing with a pulmonary edema case. 

This, being June, was the "summer" attempt.  Temps were routinely -20F and we experienced one storm which treated us to a wind chilled -80F.  My mukluks handled it all in superb style and I would recommend something along those lines if you are going to deal with sub zero temps.  If you are active and it is a it warmer, a good double boot should be fine.  Those mukluks were not crampon compatible.  Our summit attempt would have seen us in our plastic slippers...

Superusers do not speak on behalf of REI and may have received
one or more gifts or other benefits from the co-op.