I'll echo what
mcshroom says above – studded tyres are definitely worth investing in, just remember to respect the ice and adjust your riding style accordingly
The past 2 years I used 35C Marathon Winters (240 spikes) and have seen myself gain grip where you couldn't even stand. I'd been debating which tyres to get this year but have just ordered up the narrower 700x30c Schwalbe Winters – my dreams of a new winter N+1 have been dashed (the Genesis CdA 20 won't be available until next year) – and at just £16 each from Germany (£37 posted) I'm not bothered if they only last me one winter. I need to still get to work during the winter as we are a one car (+ several bikes) household and there are days I simply don't have the option to lift the car keys.