The thing that you need to get your head around within the context of the OP's original question:-
When you run, your lifted foot points down at around 45 to 60 degrees declined from the horizontal. With a snow shoe fitted there would be around 12 inches of snow shoe projecting below your toes; thus you would require an extremely unnatural extra elevation in foot lift, particularly when bringing the trailing foot forward to re-plant it.
From what I've seen of people using snow shoes, the foot is maintained in an almost horizontal position ( to keep the 'toe' of the snow shoes from ploughing in). This is more conducive to a walking action, rather than running action.