You might consider cyclocross tires. I don't know what is available now but grippy, relatively smooth, fast CX tires are used for some racing surfaces and would do well for what you want. I used to commute all winter in my days without a car on sewup cyclocross tires with a fine diamond tread. MoOre recently (15 years ago?) I had a pair of green threaded Vittoria CX clinchers that were so "sticky" they were very ride-able on almost all ice/snow surfaces (and so much rolling resistance I used to seek out sand, leavers, gravel, whatever riding dry pavement just to make the ride a little easier! If you have a local cyclocross community, I'd consider asking one of them or going to the bike shop they use for their recommendations.
Ben