Trail runners do well in snow as long as you keep moving and don't settle down. Mine are NOT waterproof (new balance, lower priced versions) and still stay dry unless I'm in slush, but it doesn't matter. They work fine wet. It's when you stop that you have to be careful and keep your feet warm/dry. I wear the thinnest nylon socks. Two pair at a time, still thinner than normal socks. They dry quickly and tend to be warm.