Would there be an inquest? Scotland does not have a system of inquests, and I can't remember if they would automatically apply to military personnel killed in Scotland?
The Scottish equivalent would be a Fatal Accident Inquiry (FAI) presided over by a Sheriff. An FAI certainly can be held into the deaths of service personnel in Scotland, such as the one into the Mull of Kintyre Chinook accident. Legislation is pending about FAIs into the deaths of service personnel abroad.
As these tragic avalanche deaths are presumably not suspicious or unexplained, and possibly not directly in the course of employment, my guess is that an FAI in this case would not be mandatory. There have been other avalanche deaths in Scotland this season, as you know, so that may be a factor in the decision whether or not to hold one in this case.