Clearly some cyclists refuse to see or chose to ignore snow and ice create an increased and entirely avoidable risk. Recreational cycling in these circumstances is at best foolhardy.
Unless I've missed it, you haven't stated what these risks are so I'll go out on a limb and suggest it's slipping which leads to crashing which leads to injury which leads to paramedics. Or, due to similar circumstances, being hit by a driver. If I'm wrong, I'll happily be corrected.
This being the case, cycling in general according to you should be banned unless it's dry outside.
No more mountain biking as in my experience, wet rocks and grass are one of the biggest causes of lost traction. In fact, the sport/activity should be banned outright. Even in the dry. I mean, what kind of idiot blindly launches oneself down a rock strewn cliffside in the pursuit of fun?
Road cycling should also be curtailed. How many cyclists cling to the corners of country lanes without thinking about the chances of hitting an oil slick or patch of leaves? That's just stupid.
While we're at it, no more ascents of Everest or k2. Might as well limit Ben Nevis to the general public too as it can be snow covered at times.
Then there's ice skating. There's an activity specifically done
because it's slippy. Madness.