It's not a "reminder" for people who've never been to the site before. Especially not when the icon isn't even visible on some devices, like my phone in portrait.
No you can't, it just turns the background yellow.
EDIT: the snow stops _but after a few seconds_. I toggled it to find out if it would turn off the snow, and the immediate feedback was that it doesn't. That's really _really_ bad UX.
I get the site has a frivolous feel, which I do like. And there's no problem with snow if you can turn it off. But it _seems_ like you can't turn the snow off, at which point it does become annoying.
And it's actually making a serious point about something I care about, so I actually wanted to read the article (which I did through the snow).