I second the idea of Koolstop salmon pad which is designed for wet weather.
Brake pad can wear very fast in wet condition. CapnSnarls already explained the reason. When this happens, the distance between the brake pads and the rim increases. Therefore, it requires more distance on your brake lever to apply the same amount of force. It is possible that the distance between the brake pads and the rim is too much that they become less effective even the brake lever hits the bottom.
If your brake has the barrel adjuster, you can tighten the cable to fix the problem on the fly. Then readjust the cable tension when you reach home. Check your brake often in the winter.
Be safe on the road.