It certainly depends on how much you really want to commute. I only do my long commute on the MUPs (22 miles roundtrip) once per week on average in winter and think studs would be unnecessary for that. I realize others want to go every day so you'd probably need studs. I've never had much of a problem picking the day I ride with the most optimal weather when only riding once a week. My short (1.5 mile one way) to the subway on streets I've nearly always been able to do a few days after it snowed although it's not always fun.

Ice from rain I've never found much of a problem as the MUPs I ride drain fairly well. Also you tend to get very familiar with where you ride and know exactly where the water pools up and hence where it might freeze so you usually ride around those few spots. There is also a spot on the Mt. Vernon trail where the water drains from a higher elevation and tends to freeze but again I know that and expect it and have walked around it on the grass if need be.

Regarding the wooden bridges, I've never had a problem if I just keep my tires moving in a straight direction and make no sudden moves. No wooden bridges on my commute are that curvy so I've never had a problem.

The problem I have had is after snow, in some shaded spots, there will be long narrow strips of ice that form with no relation to where the water drains. But again after a few years, you recognize the spots where it is shaded.