How do belt drives perform with snow?
It depends

Belt drives require some mechanism to prevent the belt slipping off of the sprockets sideways.


Early generation belt drives have guides on both sides of the sprocket to keep the belt from sliding off. This can definitely lead to snow, mud or other debris getting trapped in the sprockets, getting packed in tighter with every revolution, and eventually rendering it inoperable.
Later designs started compensating by adding mud ports, a guide on only one side of the sprocket (with other guide on the other side) and other mechanisms to allow snow or mud to be squeezed out of the system.
The most recent design has a guide that runs down the center of the belt instead of on either side (so the teeth on the belt have a gap in the middle), which should squeeze snow or mud out the sides of the sprocket and belt. From what I've heard, this is supposed to be the most difficult to clog design.


(doing a little research, number 3 is the "Gates Center Track" that just came out at Interbike 2011 and the bike I saw with it was probably one of the first production bikes of that model off the assembly line)