I would consider Bridgestone Blizzak. Not cheap but if you can't run studs the Blizzak is a great tire. I would avoid getting a wide tire, too much flotation on ice and snow will hurt traction. Get stock or narrower tire. Do you have 2WD or 4x4?
Early 1999 F350 AUTO 4x4 CC LB DRW 4.10 6.0 trans cooler, Front hitch, 2,000 hubs/ brakes, Bilstein shocks/steering stabilizer, Diesel site coolant filter 203 thermostat, EBV delete, new O-rings, new Oil cooler, RIFF RAFF FRX, Glow plug led, Pillar gauges, Lighted cupholder, Painless wiring fuze block, Harpoon/hutch mods, Removed axle blocks. Air bags, 5 wheel hitch, In bed 7 pin plug. Spare tire key delete. KLHANSEN on speed dial. 75,000 as of May 2019