Back 'In The Day'.......
I once rode home from Leeds - Wakefield, back in early 1995, which had a quite fearsome couple of days of snow (where buses were off the roads by 15:00, Churches/Schools opened up for stranded commuters
Our vans were stuck all over the country from Birmingham upwards
Come home-time (23:00), there was probably 6 - 7 inches on even the main A61 (Leeds - Wakefield)
I managed to ride most of it, weaving in/around stranded vehicles, even up Bell Hill (for those around the area, the drag from Stourton, up to the 'Jaw-Bones' & the junction with Wood Lane (into Rothwell)
On a pair of grotty old Michelin tyres ('23', I think), I had no issues........ barring a bit of snow clogging the 'guards
I only had one hill that I couldn't get up. but the snow was drifting over the fields & was deep enough to offer a good resistance
From memory, it took me an extra 10 minutes or so
Today.................
I had an experiment earlier this afternoon
Don't get me wrong, I'm not that worried about falling off, but don't want to do so, & jigger up a hydraulic STI 'brifter' (at the price they are!!)
It's the wheel off my CX bike, which is on cantilevers, so I can't use them