Rode my Intense 6.6 with Rubber Queen 2.4 front and Ignitor 2.35 rear and my Cove Stiffee with Nobby nic 2.25 front and rear around Chilterns and Swinley. the Intense was sliding about a lot, the Cove had a bit more grip. Both bikes had me sliding merrily on my back-side on packed road ice.
Gotta say the whole thing was a good exercise in learning where to put your body weight. Changing my riding style (keeping knees well bent and body weight as low as possible and shifting about way more) on both bikes had far greater effect than the difference between the tyres.
Lowering the PSI helped massively although I did then inevitably pick up a slow puncture in the Nobby. I’m 70kg and was running the front nice and squishy and the rear a little firmer.
I’d say concentrate less on the tyres in the snow, and more on the way you ride.