Check out the wet weather fun on YouTube. (with music this time)
When I was a teenager (Lambretta Li 150 followed by a BSA Bantam) I only wore what was hanging in the wardrobe. I spent most of my rides wet and cold and wishing I was back home. When I returned to biking I decided that I would get the right gear, and be as comfortable as I can.
Most important is protection - from contact with other things, mainly the road surface and any street furniture that is along your trajectory. So that means decent gloves, boots with ankle protection and CE grade armour for knees, elbows, shoulder, hips and back.
Keeping rain out, and warmth in, are next. I use a 3/4 length jacket with close fitting collar and cuffs, zip and Velcro fly fastening, air vents for the occasional warm day in summer, and removable quilted lining. Over-trousers to match. As a special treat I wear Gerbing heated gloves in the winter.
With all this gear, riding in sub-zero temperatures, or torrential rain, is not a problem.
To keep your head intact on impact, a good quality helmet, with a Pinlock anti mist system for the visor is pretty useful.
All this stuff could cost a fortune, but you don't have to buy the most expensive - £500 should get you covered.
Enjoy the video.