My experience with high desert daily thaw-freeze cycles is that it tends to produce hard ice "sculptures" in the bike lanes. If you get a hard ice base, studded tires are just about the only thing that will keep you upright. If you get crusty ice, studded tires are mostly optional. If the ice sculpture is particularly gnar, consider full suspension. I went full suspension with studded tires. It was overkill except for those ~5 days per year I absolutely needed to get to work, and the ice in the bike lanes was bad enough to be unwalkable.

If you get hardpack snow, aggressive tread blocks might be enough. I've played around with smoother center tread with aggressive cornering blocks, Nokian Mount&Ground/Hakkapeliita tires, narrow slicks, hardpan tread patterns... it's all a matter of matching the tire to the surface. No single solution will cover all possibilities, and it's critical to match your tires to your most frequently encountered condition. Be mentally prepared for some trial and error.

IMO, a narrower tire is better than wide, within reason. Narrow tires tend to push through snow and crust.

As to why fixies are superlative foul weather bikes:

• drivetrain components wear together: run it until the everything is worn to a nub (if you aren't into maintenance); replace everything together maybe every 7 years; clean and lube the chain when it gets noisy
• way fewer fragile moving parts
• dead simple drivetrain that performs perfectly even when neglected, always works regardless of sand, ice, snow, salt, foul language, or bad hair days
• gravel gets into the drivetrain with the snow and ice? fixie DGAF, unlike belt drive and cassettes
• on rim brakes, less road grit abuse of your braking surfaces because can stop with the rear wheel
• fixies are generally a much lower cost bike to start and you can have yourself a winter beater that will take all the abuse and keep going; tons of choices on the used market
• cheap chains, chainring, and cogs
• changing gear ratio is cheap
• direct connection to the rear wheel acts like traction control: easy to start and stop when slippery; when your front brake becomes useless because of low traction, you can still control speed through the pedals; inertia in the drivetrain carries your stroke through TDC/BDC, making it easier to maintain a smooth stroke in slippery conditions (helps keep you moving and upright); easy to feel when the rear wheel is losing traction, if your rims get iced over (and they will), you still have some braking capability
• you'll feel like a kid again doing massive skids down huge snowy hills
• easy trackstanding at stops: no unclipping/clipping back in (less chance to clog up the pedal and cleat), no putting your foot down into car snot, no putting your foot down in an ice patch and slipping
• the time and money you save on maintenance adds up quickly; get yourself a couple sets of wheels and keep them ready for various conditions; use the same rims for rim-brake bikes to keep your sanity intact
• disc brake fixies are a bit more rare, e.g. Salsa Stormchaser 1x with a White Industries ENO hub; disc brakes expand your capabilities, ease wheel swaps when using different rims, and improve all-conditions braking
• ^that said, I only ever owned a rim brake fixie and never missed my discs even in the gnarliest snow and ice; unlike all my other geared bikes, I've never fallen when winter riding my fixie; actually, I've never fallen on my fixie, period, and I credit that fixed connection to what the rear wheel is doing
• climbing hills is like being on an escalator: because the inertia of the drivetrain carries the pedals over TDC, a fixie just rips up hills; on a 25 mile one-way work commute, my top speed was down 3.5 MPH, but overall average speed was up ~1.8 MPH, with 1400 feet of climb each way

I resisted fixies for a long time despite hearing all the benefits. The story of that fixie pictured in my previous post is here: https://lemmy.world/post/27619326/16157725. VT, OR, UT, WA, MA, and CO winters have never given me any troubles on my fixie with the correct tires for the conditions.