I just participated in a mismatch test with winter tires on the rear of a BMW 328i and it was eye-opening. A test was set up on our test track to see how all-season Michelins (Michelin HydroEdge) on front with Dunlops (Dunlop Graspic DS-3) on rear would handle in an emergency maneuver.
The cars with all four all-seasons or winters both handle similar through the slalom, with the winters having a bit more time in transition from left to right and vise versa. It wasn't less grip, just felt more like jello under the wheels than rubber in interchanges. Nothing you couldn't get used to. It was about 55 degrees out.
The trick was when we tried to go 40 mph through the slalom with the mixed set-up and 60 mph around the large skid pad. It was controllable (although the oversteer was pretty intense) until we had to go back the other direction after the large skid pad and lift off. I would say there was about 50/50 chance of complete loss of control with the oversteer.
What I found was that it wasn't a problem with grip, the winter tire did just fine when it was on a car with all four winter / snow tires. The problem was the difference in how the tire reacted to direction change and lift-off over steer. With all four tires reacting at the same pace (think spring rate or squirm) it was in phase with itself. Think of a building in an earthquake...that tread squirms and reacts to the input of both the car and the road and sways accordingly. With the front and back reacting differently (one a steel skyscraper and the other concrete), it really threw the car out of whack and on my test with our professional driver driving (I was the passenger) we did a 270 degree spin at 50 mph...after three hard oversteer switchbacks. Interesting to see it in action. So don't mix drastically different tires on a car. Winter to all-season, all-season to summer, etc. It felt fine at normal driving but that first emergency maneuver and you are in the ditch or worse!