I can't echo this enough. About 15 years ago, I went out with DH and 3 other riders. It was about 60 degrees and partly cloudy. About 3/4 of the way through, the skies opened up. I had on knickers and a wind jacket and DH had a cycling rain jacket. We refused a ride back to our car and rode about 7 miles there. By then I was shaking and soaked. DH was fine. It had gone down to about 53 degrees, too. Our car was parked in Concord Center, right in the center of town, where tourists stop and look at monuments, etc. It was before we lived in Concord, and we had a short drive home to the next town. I stripped right in the front seat of the car and wrapped myself in a beach towel DH kept in his car for emergencies, and put the heat on me, full blast. I was still shivering 2 hours later, despite several cups of tea, a hot shower, and getting in cozy clothes. It was scary, to say the least. After that, I bought a rain jacket, helmet cover, and eventually rain pants, which I wore on a tour about 2 months after this.
I was reminded of this last Saturday, when I was xc skiing in a light, but steady snow. I started feeling cold, which is most unusual as I usually am hot. I kept saying, it's OK, we'll be done soon, until I realized I was wet, getting hypothermic, and I was doing what we had been taught about in AMC Leadership training... poor judgment because cold is setting in. I stopped and thankfully, I had my soft shell in my pack, which I changed into. Immediate relief and I was glad I had the forethought to pack it.