I hear this frequently: "I can't wait for the weather to get better so I can cycle outside". And, as somebody who lives in California, it's hard for me to give an answer without relying on the experience of others because our weather is fairly nice out here... although most people think of San Diego weather when I talk about living in California.. and Silicon Valley is very much not like that. Furthermore, I was hoping that my awesome coworker Chris who is at least as insane as I in many ways wouldn't have broken his ribs at the beginning of winter. Because he got a Surly Pugsley to bike in all winter but he's presently laid up.
Oh well. I guess I'll just plod along. This is the Internet, after all. I could start making stuff up.
I find the notion of being stuck indoors in nasty weather to be depressing. I am not water soluble and am capable of producing a certain amount of my own heat. And biking in crappy weather on a bike is actually not a big deal. It's mostly a game of gearing up. I've got the gear for 30s-and-40s cold temperatures and rainstorms. Bikes do not hydroplane, by the way. I don't have the gear for snow, but that's only because we don't get snow around here.
However, they make studded bike tires for normal bikes. And they make the Surly Puglsey and a few other 'fat tire bikes' that have extremely wide tires that pretty much mean that you float atop the snow as if you had skis or snowshoes instead of sinking into the snow. And if it were snowing, I'd probably just need to add another layer.
Let's take a step back and compare, however. If I'm running in the snow, I can layer up in exactly the same fashion. I can hike in snowshoes or do cross-country skiing. On the other hand, and I had a reminder of this last weekend when I walked to the grocery store instead of biking or driving to the grocery store... a bike has carrying capacity. If you want to carry a thermos of tea, extra warm clothes in case it gets colder, have a place to put your clothes if it warms up a bit, etc.... well, all of this is easier on the bike. I don't notice the weight of a gallon of milk, 2 pounds of tea, a pound of salt, 3 onions, and some Indian ramen if it's in my panniers. But to make me carry it, I notice that it's there. If you go running prepared for sudden rain squals and it stays dry the whole time, that sucks a lot more than if you go biking prepared for sudden rain squals.
Getting caught by an unexpected stint of bad weather is unpleasant... but being prepared for bad weather while biking is not bad at all. So don't wish for better weather, get better at biking in bad weather.