It's snowing again today, but that doesn't stop the running.
The cold weather is something I'm fairly used to - I have gloves and a hat, and wear two layers.
But snow and ice mean you need some extra kit - I use my off-road shoes (they have little studs for grip, more rubbery and smaller than football boots, but similar - and they're water-proof lined), and if it's very icy, I use spring grips. I get all the traction I want that way - it ends up feeling like running on sand.
If the snow is very deep, I'll wear my gaiters - they cover over the lower legs, and keep the snow out of the socks.
As well as the obvious stuff, you really do need sunglasses, even in overcast conditions. The glare off a field of snow is horrible - it feels like arc-eye if you run too long without sunglasses. I've resorted to running with my eyes shut before - now I always wear my sunglasses in the snow.
It takes much more effort to run on snow than usual. Off road running on snow is even harder - the frozen lumpy ground is obscured by snow, so you don't know what angle your feet are going to strike. That means you have to be prepared for anything - it's a slower run, and your legs have to ready to react to bad ground.
So, all wrapped up - I'm off!