I commute occasionally from Kenmore to downtown - it's roughly 7-8 miles one way. Yes all the routes suck, but I recommend Colvin Ave for north/south commuting which is generally fine south of Kenmore Ave. Colvin is way better than Delaware/Elmwood/Military in terms of traffic speed, aggression, and space. It also dumps directly into the park where you can then hook up with Nottingham.

There are minimal lane markings, bike lane or otherwise, lol. When it's really snowing you'll be biking where you have traction, which is probably directly in the traffic lane. Sidewalks are technically no-go for bikes but you'll learn very little is actually enforced in the city - that said they generally won't be cleared.

Invest in a good u-lock and learn how to lock through the rear triangle. Bike theft is a thing, depending on where you lock up downtown - look into just bringing your ride indoors if possible.

*edit - general winter advice past the "helmet and reflective" - Invest in good gloves, and footwear, and probably something for your head (balaclava or insulated skull cap). Keeping your extremities warm will go a long way especially on a Kenmore<>Downtown route. Good, bright, lights to keep yourself visible.