Here's a slightly different perspective on "being sensitive to the cold" based on some atypical, empirical, first-hand evidence...
In 2007, got *very* sick (fine now, thank you).
Started at 180 lbs, and was always "plenty warm." Too many covers on the bed, happy in a good vest @ 32 deg. F.
Four months later, summer of '07, I'm down to 130 lbs., and the meds are trashing my circulation, as well.
I was FREEZING for then next two years as I worked back to normalcy. Fingers, feet, arms, everything. I was shivering as soon as the hot shower went off. I couldn't take Maine in August. I have this expedition-grade down parka that's good for McMurdo station. I wore silks under my dress clothes to work from October 'till May. Never got warm.
Roll out to today, I'm at 157 lbs and in decent cardio-condition (thanks, bike). I've got a normal level of body fat (BMI = 21.5).
Now I don't get cold like that anymore. But I remember...

I think it's all about body fat and capillaries. Both tend to "retreat" with age, but keeping up the cardio may be the best attack - warm stuff running through the tissues.
Otherwise, refer to rule #5 ... <grin>