"Snow day" is an expression.
The vast majority of Canada/US still have snow. When there is a "snow day", most people do fun things. It's treated like a day off - from school, work etc... Often, snow days might start out bad, but after awhile the storm passes and roads are cleared, so people head out and have some fun - skiing, snowmobiling, visiting friends, playing etc...
It probably also helps to remember that a lot of places, northern US and pretty much all of Canada, have a VERY different experience of snow days, than those of you that don't see much snow. You get an inch and the whole city shuts down

Here, it takes pretty much a blizzard to shut everything down. Most storm days, the schools shut down, but everything else is still open (so you can still go skiing, shopping, to the movies etc....).
So all people mean by saying they treat it like a snow day, is just that they're looking at it as a free day off, to go have some fun. Around other people.