Am I going to run into any problems if I leave my all-seasons on the front but put dunlop M3's on the rear for the winter up here in Minnesota?

 

Personally I would go with all four. Seeing that most of your stopping power is up front I would feel better having them all around rather than just the back end

 

No, run all 4. You don't want understeer if your front tire slip and your back still grip.

 

I agree. Just get 4,

 

All four corners! Allways! Snow tires don't just provide traction for acceleration, they provide stopping and turning traction too. All four wheels participate in stopping and turning.

Also, as someone already ready mentioned, you can seriously impair the handling of the car with massive understeer with snows on the back only. Or, massive over steer with the snow tires on the front only.

Lastly, even on dry pavement modern snow tires rely on high tech tread compounds that are vastly different from a summer/all-season tread compound. They are much softer in all weather and generally molded to a greater depth with a more flexible sidewall. The result is a much "squishier" tread on dry roads but life saving traction on cold wet surfaces. Mixing with summer tires can produce some truly wierd feel even in a change of direction as mild as a lane change.

 

Dangerous with snows on rear only. Go for winters all-around and have equal stopping power and manueverability on all fours.