Surely no road tyre will be a match for the hazards of winter cycling, such as the Wheatsheaf manhole covers of doom in the wet or invisible black ice. Even standard mtb tyres would struggle in winter – hence the need for steel-studded tyres.
Unless you have cantilever brakes, not even cyclocross tyres will fit, so you’re a bit limited.
The Vittoria Rubino Pro is a good value high quality tyre with a reasonable amount of tread, and can be bought for £10 on Amazon. Not bad for a 150 tpi 200g foldable tyre – and they’re meant to last for a few thousand miles.
Always a trade-off between weight, grip and puncture protection. Gatorskins are good all rounders with the hardshell variety offering a very well protected tyre. Use these on the commuter to try and minimise time spent at the side of the road. Just make sure they’re foldable.