Snow has a tendency to build up on windscreens and leading edges, restricting visibility and changing aerofoil shape. The result can be a wing with a strong disinclination to generate lift. A colleague of mine once nearly ended up a hole in a mountain in Norway in an HS780 as a result of this fascinating phenomenon - and that was supposed to be de-iced! (Anti-icing, maybe, would have worked better.)
Also, even very light snow effectively puts you into IMC (imagine flying through the old windows "stars" screensaver) and you have the idea. If it starts sticking to the windscreen, you won't see a thing (happened to me once in unforecast snow, scared the heck out of me - flew out of it on instruments and thankfully it cleared quickly).
Of course there are fully anti-iced aeroplanes which can handle this, but for the stuff most of us fly, it's likely to end in tears.
Flying *over* snow once it's stopped falling is just pretty. Things look slightly different so a little more care in navigation is needed, low level turbulence tends to be minimal and so long as the runway you use is de-iced (or you've taken appropriate care and applied necessary safety factors) it's really very safe and enjoyable.
G