You need to have similar traction on all four wheels. Especially you do NOT want lower traction on the rear wheels. You will spin and not be able to see or avoid whatever you are spinning into!
I "threw away" the nearly new stock Goodyear Integrities last October, and put on Nokian WR "real" all season tires. I had no problems this winter. In fact, last weekend we had a blizzard. I drove on a 70 km/hr or 45 miles per hour highway and didn't slip once. That can't be said for many other drivers - passed by one clutch of 10 cars that slid together in a cluster and another full sized PU that spun into the median. Even the new Blazer ahead of me would spin up his rear wheels and slide sideways 2-3 ft every time he started. MORONS! He had 4WD and didn't even bother to engage it, hence was sliding on the ice/snow! All this in just two miles of road!
This drive DID drop my mileage average, of course.
But not because of the Nokians. They didn't decrease the cars' mileage at all. It's was the short trip.