I used to hate exercising on the cold oklahoma mornings (but the Army gave me no options). One morning my legs almost locked up. I think it was about 15 degrees. But we were better off than the marines.
Sounds like you really need to warm up a bit more before you ride.
You have the hat, so you might want to try a neck gaiter too. The blood can cool a bit on the trip through your neck. I learned this trick in Officer Candidate School.
Try some warmer knickers. I wear my wool knickers if the temperature drops below about 65 and wear those down to the mid-40's.
On cadence.
The idea that 100 is the magic number became vogue with Miguel Indurain. He was the first person to truly dominate the tour for several years in a row. Apart from his general physiological freakiness (resting heart rate: 30), he used a very high cadence for the time. Lance Armstrong took note and started to do the same. Now, everyone does it. Spinning classes encourage it because a higher cadence is a good way to get your heart rate up quickly.
I can do 100 and once held 120 for a couple of miles just to see if I could do it, but I prefer somewhere in the 85-95 range. I bow down to OakLeaf for hitting 160. That is truly awesome.
If you can tick along happily at 18 miles an hour at 70-80 and you don't have any knee problems, you are probably ok.
re-cur-sion ri'-ker-shen n: see recursion