Rear End Alignment? Can out of Alignment effect winter traction?

I have lived in Michigan my entire life and owned dozens of vehicles and have never had one react the way my Prius does on snowy/icy roads. I could not quite figure out until this last snowfall what exactly is happening that is making it uncomfortable.

As soon as the road gets hard packed with snow and/or is icy the rear end of the Prius wants to constantly wiggle around a bit. So much so that you have to continually make subtle corrections to the steering on the front end to make sure the car travels a straight line.

After thinking about this more and paying more attention to driving on dry pavement the car does seem to wander a bit when driving on dry roads as well but it is very gradual and not nearly as abrupt as when on icy roads.

Sorry for the long explaination, but I was wondering if it is possible the rear end of the car needs alignment? I don't notice any strange tire wear but I have not had these new tires on the car too long.

Thank you for your help.