Bottom line. . .
Putting snow tires just on the rear will affect handling, things like turn in, under steer , etc. How much depends on the specific tires.
And how much it will require the driver to adapt depends on the driver, road conditions and speed. In the upper central Midwest, many used to do this including me. It was not a good solution for ALL drivers since many did not know what to expect in handling changes.
Example:
Cruising down a snow packed road at even at a steady 45 to 55 MPH, you might find the rear of the vehicle wanting to swap with the front. Sort of a slow drift and this was just going straight down the road. Kind of fun actually. You could control the amount of drift by modulating the gas pedal. But all this told me was to slow down for the road conditions and adapt. This was dangerous for some and they might panic, over correct, or hit the brakes, and spin off into the ditch or hit a tree, a light pole or someone else.
One thing for sure. . .. this kind of thing required constant attention to driving . .. . not checking a text message on the cell, or playing with music selections on it or a USB drive.
I don't know that I generally trust driver's skills and habits to recommend snow tires just on the rear. All 4 wheels is definitely safer.