I used to live in Montreal, and snow was a norm for more than half the year. People therefore embraced the snow and made all sorts of festivities around winter. There is one very popular activity which is called Sugar House (Cabane a sucre in French), where you pour maple syrup over fresh snow, take an ice-cream stick and roll the sticky maple syrup with snow into a ball. What a yummy cold treat! :)
The best snow-based activity I think is building snowmen. Unlike with skiing and other snow sports, you do not have to travel to some holiday destination or facility. Building snowmen can be done in your garden or any anywhere it is snowing. You don't need to pay to do the activity, and you don't need any additional equipment other than the than the things you have at home - a hat, scarf, carrot, etc.