I've ridden in my share of cold rain. I had a 7.5 mile commute every day, and had no car. I did a lot of experiments in handling rain, and discovered that there is no good way. Oh, some ways are less bad than others. So, the last time I got caught in a rainstorm, I took shelter under a portico.
The main way to handle it is to keep moving. I got caught in a rainstorm on a mountain bike ride one day, and just about froze on the way down the mountain. I had to get off the bike and walk in order to keep hypothermia away.
Rain is really hard on the machinery. Especially on beach bike paths; sand gets picked up by the tires and thrown into everything. I hate that grinding feeling of sand on the chain.
I will say that fenders help a lot.