Two wheels - slick or MTB just don't grip on ice. If it's a rough road surface then you are ok - eg big chippings, but any smooth stuff...you have no chance....
I've come off more on an MTB in the ice than a road bike - all on tarmac. If you can guarantee your route is on well gritted roads, then you should be fine, just watch junctions and side roads - ride where the cars are - if that means a good secondary then do so.
If you hit ice, then it's a chance that you will stay upright. My estate was a skating rink - even my 1.5 tonne car found it slippy. If you see the ice, and are going straight, at a slow speed, you should get over it. If you are riding briskly, don't see a patch, and are mid turn, then you are off. I've lost a front end 3 times on one ride 1) 30 mph down hill, straight road......front just went.....I slid for ages, luckily early am, no cars. 2) A little later, hit ice again going up hill, off into the ditch - not too fast. 3) - Again slowish speed off onto grass. It was no. 1 crash that did the damage...... gravel rash, torn clothes, scraped bike.
One thing that is dodgy, if you come off in high traffic....
Think about it.....one crash can have you off the bike a whole lot longer than a few days in the car/on the bus.....
Main thing - frosty and dry/sub zero is OK - just watch for damp patches. Wet/sub zero = main ingredient for accidents. I'll ride if it's been dry and frozen, but not if we've had rain/snow showers then frozen.
Be careful !