Why its harder to run in the snow

Today was one of those days when all the roads were covered in snow, which is bad for driving and even worse for running. A few steps in that salty slush and you'll be slipping all over the place. What I've found is that snow sticks to the bottom of my shoes and stays there, so rather than my rubber soles trying to get traction with snow, there is just more snow trying to get traction with the snow. This drastically reduces the coefficient of static friction between my shoes and the road, causing my feet to slip every step which gets really annoying after about 20 feet. Also less frictional force means less effect from newton's third law and more energy wasted every step making running a tedious task at best.