It really depends on the snow and the tyres you are rocking... the wet sticky oatmeal snow I was plowing through today was about as vigorous as it gets but I was riding on roads other cyclists would have avoided as they would have sunk down into this.

Higher accumulations of lighter snow are not as hard to ride through as wetter and more compact snow...

My Nissan Sentra rolls on Nokian Hakka R tyres... the stability is incredible and I have passed a lot of stranded AWD cars and trucks and ridden though all our northern mountain passes in winter and even during major storms with few worries.

Nokian winter bicycle tyres are better than their car tyres when it comes to travelling on ice.

I'll add another endorsement for the Nokian W106 tires.
I bought a pair after looking at Peter White's website - he recommends these for paved roads with periodic ice. Winter falls on ice or turns ended; I also had good traction climbing hills and could steer and brake much better.

To the OP - you also get interesting reactions from people shoveling out their cars. I'd usually tell that the bicycle is much easier to dig out than a car. Most would laugh but some seemed serious and very annoyed.

AKA as "high centered" among 4WD enthusiasts.
I've seen it happen many times to new drivers of 4WD's who blindly believe they are invincible, instead of using some basic common sense. On one occasion I was in the passengers seat while the idiot driving tried to climb it over the 3' bank of snow along the side of the road left by the snowplows clearing a blizzard. And here is the punchline: We were driving a dealer's demo!

Many years ago driving with a friend in his 4WD jeep on a "black ice" day, I commented that he should slow down and keep his eyes open because there was a decent amount of ice forming. His "don't worry, I have 4 studded tires on this" said just about 2 minute before the road curved and we didn't, ending up tilted about 45° in a ditch. It was a cold walk in the rain.

Ugh! That reminded me of one early morning pre-dawn drive to the ski area in my Jeep.

We were cruising along I-70 @ 10,000' doing 45mph on wet road (I thought) when I noticed up ahead a car pulled onto the road from the right. Odd, I thought; I don't recall an entrance ramp there. As I slowed to allow the car to merge, I suddenly realized we were on black ice! I managed to stay in my lane and keep the headlights pointed in the general direction of travel as we slid around trying not to rear-end the car merging. I also realized (from the tracks) there was no intersection; That car had run off the road and slid back on! At this same time I saw that the sleeping idiot (ex-GF) in my passenger seat had removed her seatbelt. So there was absolutely nothing that would have stopped her from going into the windshield if we had hit the car ahead.

metrowest Boston gets a lot of road salt and plowing so I guess we have it easy. just have to watch out for the slush at the shoulders

Exactly what I do too. The homemade ones with the sheet metal screws would not make on the pavement for my commute. Just like TSL mentions here, factory carbide studded tires are not that expensive and you just put them on and fagetaboutit. They last.

Although I rarely see clear pavement on my winter commute or recreational rides, with a properly laid out DIY winter tyre there is little to no stud engagement until your tyres go off camber so in that respect they handle clear roads quite well.

They cleared the roads here last night... we got almost 10 inches of snow in rather short order and then warmer temps turned that compressed snow into oatmeal.