Full disclosure: It is not snowing here currently. This brings me to the first reason I like snow: there is no escaping winter here, so it is going to be cold, but days when it can snow are warm days. Other times (such as now: overnight forecast of -30°C, windchill warning of -45°C) it is so cold that it cannot snow. I always enjoy watching people get their heads around the idea of "too cold to snow". (It is also fun to watch people realize that in the winter months, there is a very good chance that a clear, sunny day will be much colder than a cloudy day.)
The best kind of snow is big fluffy snow -- the sort of snowflakes that look like you could pick them out of the air one at a time with your fingers. The things I like about snow tend to be centred around that sort of snow. Most of the things I like about snow have to do with being in the city, too, but for all I know you get the same effects in the countryside. I'm just not there.
I love how snow makes everything so quiet. Even on a downtown street, having a few inches of fluffy damping material turns down the world a few notches. It's very much a "something is wrong here -- what is it?" feeling at first, and I think that's why it's so neat.
Similarly, snow makes everything look clean. Even a well-travelled road will just be white to light beige right after a snowfall (and before the salt and sand trucks come out).
Snow takes away urban boundaries. Areas that were parking areas become unmarked and then taken over by pedestrians; unplowed sidewalks and quiet streets make pedestrians take to the roads; the design of parking lots suddenly becomes up to the people parking in it.
After a fresh snowfall, the world is lit from below. I've read that the unusual lighting circumstances of a snowy winter is one of the things that triggers seasonal depression, but for me it's as though the world has been lit up with fill lighting instead of key lighting. This combined with the sound change and cloud cover makes the whole outside feel like a strange, big room.
Lastly, after the snow's been around a while, it's plowed into piles and left for spring. This has always amused me. We like to think that we've pretty much trumped this "nature" thing with our new-fangled "civilization". Usually when we get reminders that it's still a pretty even balance, they're destructive -- hurricanes, floods, hailstorms. As much as I love big weather too, the piles of snow are a more peaceful reminder that there are some things about nature that we just have to get used to -- yes, we've built a whole city here, but five months of the year we're going to have to take this stuff and put it in piles and try to pretend it's not there.
nyxie thinks i'm nuts for liking snow, and most people think of winter sports when it comes to snow fans. Me, I like how it makes you pay attention to things not being the way you expect anymore.