Do backcountry skiers object to snowmobilers in ski terrain?

Local snowmobilers are advancing the argument that backcountry skiers and snowmobilers can share the same terrain without conflict. Essentially they are saying snowmobiles do not degrade the quality of the backcountry skiing for skiers, backcountry skiers do not object to using the same terrain that snowmobiles use, and backcountry skiers do not need terrain that is free from snowmobiles.

So I am soliciting comments from backcountry skiers on the attitudes of backcountry skiers.

1) Do backcountry skiers object to skiing the same terrain used by snowmobilers? Or, do backcountry skiers object to snowmobilers shredding their ski terrain? I'm not talking using a snowmobile to access ski terrain. I'm talking about snowmobilers in the terrain that backcountry skiers are descending.

2) Does snowmobiling degrade the quality of the ski experience for backcountry skiers? If so, what is it about snowmobiles in ski terrain that bothers you? 

3) Is it desirable for backcountry skiers have terrain that is free from snowmobiles?

Please make comments expressing your how you feel about the above questions.