Besides the practical, physical advice from others on equipment and gear, I recommend a mindset reset that billions of people around the world ride bikes rain or shine every day -- old, young, rich, poor, male, female, etc -- and have for generations.

I remember riding in Vietnam during monsoon season. When the rain started, everyone pulled over a few seconds to put on their ponchos and started riding again.

I suspect that we who don't ride regularly are the exception.

Here's a podcast episode of mine of a school principal who wrote his bike to school every day in Alaska, often below 0F http://joshuaspodek.com/guests/jethro-jones. He was pretty fun about it.