Nice shots, Scot.
In terms of settings for the dug, two things to consider.
Most cameras focus on whatever is in the middle area of the frame. I note at least one of your shots has the dog right of frame, hence the background might be getting focused upon. Initially, just try to train the centre of the 'finder on what it is you want to be in focus. Some cameras have a focus lock - usually a "half-press" on the shutter button which will let you focus on a subject centre frame, half-press, then re-compose the pic for where you *really* want things and press all the way to take. Or just keep it centre and crop later on the computer
Second thing is shutter speed. If the dug is moving fast, you may get blur if the camera is using a "slow" shutter speed. Most modern digitals etc give little or no control over this, although if you have a "sport" mode, that'll bias the shutter to a faster speed. If the lighting is bright enough, this shouldn't be a problem. One thing to try is "panning", where again you try to keep the subject constant in the viewfinder frame, moving the camera in sync with it. Then it's the the background which blurs, rather than your subject. Tricky to master but worth trying because the results from this can be epic - really highlights your subject when you get it right.
Final point. Again, lots of auto cameras can tend to under-expose with snow, making your pics a bit dark. Think yours on here seem OK, but if this happens to you, the set your "EV" or exposure compensation to +1 stop - this forces the camera to let in slightly more light than it actually thinks it needs, which compensates for the brightness of the snow which initially forced it to allow less light in. IYSWIM !!