an ND filter would not help, as it would evenly reduce exposure across the frame (unless you had a dog-shaped-cut-out in the middle of your ND filter).
a CPL would, as K3nt noted, cut down some of that glare. however, most CPLs give you at most a 2/3 stop difference ... it'll help, but it won't kill full-on-midday-sunlight.
you can probably recover some more highlight if you shoot with very neutral settings (rather than the standard tone curve which is pretty amped up already).
the more important thing is to accept your camera's dynamic range for what it is, and learn to work with it. if you have to shoot in snow, don't do it in the middle of a bright sunny day, where you're running into peak intensity on the snow. go into the woods and shoot in shade. consider using supplemental lighting on the dog (flash unit could help, although it won't keep up with your 7D's 8fps shooting rate). if you get really serious, get a higher-output flash unit that can actually compete with the sun (Elinchrom Ranger RX's). that's how ski and snowboard photographers get properly exposed and reasonable dynamic range shots.