Rain pants. I was a mormon missionary in northern Japan, and we rode mountain bikes everywhere, regardless of weather. Typhoons, blizzards, compacted ice and snow on the ground, all of it is actually quite easy to bike in. Assuming you already have a water proof jacket, about $30 is all you need to get some waterproof pants that can quickly be pulled over your actual pants and keeps you perfectly dry, and then removed at your destination.

Weather should really be one of the least concerns on anyone's list for cycling.