You dress up better. For the past several years, biking was the only way I went to work, the only exception being if my bike was in the shop for repairs when I'd take public transport.

You'll notice that regardless of the weather, people bike. Chuck some rain pants and a rain coat on, or carry an umbrella, or get a bike poncho thing, or all of the above. It's not hard.

If it's seriously shitty weather, the public transport is a bit more full than otherwise, but still people are out biking because that's how you get from A to B.