Having had a couple of kids attend Hamilton, you will need a decent pair of waterproof boots. Last winter was mild. But remember that CNY averages 150-plus inches of snow each winter. Duck boots are popular (particularly those that have a heavy lining). Hunter rubber boots are popular for girls, particularly in the spring when all of those inches of snow melt into a foot of slush. Timberlands are popular for all.
The road crew at Hamilton does a pretty nice job of keeping the paths, sidewalks, and roads clear. So a lot of kids just wear sneakers to get around. Hope this helps!