Fenders are a requirement in the dirty, sandy, salty, wet winter months. They protect your clothing and parts of your bike from winter slop.
These cover most of the wheels and require installment to eyelets and frame/fork mounts. They offer the most protection and can be sized to a road or MTB wheel. Don't neglect cleaning them.
Caveat: On very snowy, slushy days, they can get packed with snow and may require a bit of emptying on a longer ride.
Lacking attachment points? You might be able to rig them up with some help from a bike shop. Alternatively, you could DIY fenders from a heavy plastic (think political signs) and some zip ties.
Do not offer as much coverage as full fenders but allow for ease of switching between bikes.
TIre size and type is personal preference based on experimentation in the snow.
Some enjoy cutting through the snow and making contact with pavement. Try to find a tire that has a pattern good for wicking water.
CX style tire that provides a bit more grip with knobs but also allows for a bit more speed because of higher tire pressures.
26", 29" (MTB):
Big knobs, low pressure allows for a lot of float through snow.
Studded tires (700c and 26"):
Have small metal studs embedded in tire to provide traction in icy conditions. Increase in confidence in harsh weather conditions. Most expensive type of tire and also heavier.
Flat pedals and adjustable straps are good for accommodating wider boots in winter months.
Neoprene booties are a good addition to cycling shoes in order to continue to use clipless pedals. Can add toe and footbed chemical warmer if going on longer ride.
Lights are important as drivers of motorized vehicles are not always expecting to see a cyclist in the winter months.
My recommendation is a small blinking LED on the handlebars (to be seen) and a stronger light on the helmet (to see). Conditions can rapidly change in a few hours and being able to illuminate your path can help you avoid obstacles (ice, potholes, etc). The higher light position on the helmet allows you to be seen over snowbanks.
A good rear red flashing light is a good addition as well.