Honestly, people's account of winter will vary depending on how prepared they are, how well the maintain their vehicle, how skilled a driver they are, how often they have to deal with morning rush hour, and the routes that they take through town.
I have a collapsible snow-shovel (used once in 10 years), booster cables, tow strap, and a few other things in my vehicle. I use the booster cables most often and almost exclusively for other people. Generally, I don't need this gear because I keep my vehicle maintained well.
Maintenance mainly includes a good set of tires. I run ice tires (without studs) in the snow season. There isn't a place in town I haven't been able to get to in town. There was some freezing rain that left ~1/4" of ice on all the roads one evening, and the 'worse' ones around (Austin Bluffs Hill comes to mind amongst others) were not a problem. (I have chains, and haven't used them in the city, yet)
Skill in driving in snow and ice pretty much comes down to keeping your tires from slipping. Don't accelerate so hard you break traction, plan for longer stopping distances, take corners much slower, etc. The worst of roads is like driving with a 64oz Big Gulp on your roof: Start, stop, or turn too hard and it spills (except on bad roads you slide or spin out). Though even skilled drivers can be thwarted by unprepared/underskilled drivers.
While I love driving in the snow, traffic makes it interesting. You have to beware people driving too fast for conditions and their vehicle's capabilities. Drivers who don't realize that bridges are often icy when the rest of roads aren't. Drivers that don't slow enough before they 'attempt' to make a right turn, and so on. People get stuck on hills in their Jeeps because they fail at the above points. Give yourself plenty of time (set an alarm earlier) to get to where you are going if there was snow overnight.
Going up and down the interstate is usually not much of a problem. I know a lot of 'back roads' so I avoid the heavy traffic areas when I can. Some places you just can't avoid going through in parts of the town (we've a few large parks and some other things that cause issues).
Having said all of that: "Generally when we get snow, have a shitty, icy morning and then the main roads are mainly just wet by late afternoon."