Phil - the toms will still strut and gobble, but the hens will change a few things:
1) Their eating habits will change, in that they will concentrate on the most convenient/easiest food source they can find.
2) They will often head to the fields, where the snow typically melts the fastest - this will allow them to find new shoots and any worms/bugs that may be in the fields.
3) They will typically follow the path of least resistance - so start looking on logging roads or well-worn deer trails.
As for the toms:
1) The toms don't like to strut in snow that's too deep because their wing feathers get wet and can freeze at night. They will move to areas with less snow for strut zones - and in my experience they will continue to use those throughout the season (and these may be completely different than 'traditional' strut zones where you typically find toms).
2) They may change roost trees and opt for those with less snow and/or ice. These may or may not be temporary, it will depend on how many things the hens change (see above).
Good luck.