The Collaborative International Dictionary of English v.0.48:

Mush \Mush\, v. i. [imp. & p. p. Mushed; p. pr. & vb. n.
   Mushing.]
   To travel on foot, esp. across the snow with dogs. -- v. t.
   To cause to travel or journey. [Rare] [Colloq., Alaska &
   Northwestern U. S.]
   [Webster 1913 Suppl.]