There are hardcore cyclists who bike in the snow. That doesn't come up (or, rather, down) here, but we do get rain. A lot of it in the winter, usually. And you don't need to be particularly hardcore to handle it.
The first thing to know is that the usual margins of tolerance are smaller. If it's the first rain in a while, oil on the road will be floating on the surface, and both you (and all other vehicles) will be more prone to slipping, and less able to stop short. First rain or not, it'll take you longer to stop (with most kinds of brakes), because your tire is wet. Your visibility is decreased, especially at night. Keep all this in mind.
The next concern is keeping dry. Having wet pants and wet shoes for hours isn't fun. But you can get water-resistant, breathing rain jackets and pants, as well as helmet covers, and zip-on covers for your shoes (don't walk in them, though, or you'll wear them out quickly.) All of these work will last longer if you treat them with spray-on waterproofing. Don't store them wet -- you'll want to plan ahead that you have someplace to hang them to dry at your destination. All winter long, I keep all of these in my bike bag.
Finally, you want to keep your bike as dry as possible as often as possible. Park out of the rain, if you can. Towel it off when you get it back someplace dry. And lube your chain often.