Historically one of the ways that I saw how well my Synthroid meds were doing was the dryness on the back of my hands. It was correlated with a lack of energy... but I didn't really notice other hypothyroid symptoms. I've never been cold, really. My friends and family have noticed and poked fun of me for it. I can stand around in the cold in shorts and a short-sleeve shirt and not feel the cold. Well, I felt it, it just didn't feel that cold.
I've started taking K2 (Carlson's 5mg twice daily) and I've noticed my skin has lost its dryness. My hands are fine. Not baby-smooth, but not dry like it's been in the past. I've also been eating better for the past couple weeks so there's no guarantee there of a correlation.
I'm also off Synthroid, because I need to see a doctor. My doc won't refill the prescription til I make an appointment, and he's in a different town, so that's for crap.
And, being off Synthroid, I've noticed the cold. I don't know if I noticed it when I was a kid, or what the deal was. I've been in Texas for so long that there's not enough cold weather to really notice it. But now my AC works. Used to be that I'd have to set my car AC to LOW (which means max AC with the fan at full blast) before I felt cold, and even at 64 (the next setting above that) it didn't feel chill.
I'm changing a lot of things. I don't know what's doing what. My plan is to try to improve my diet and habits and much as possible, and then later start re-introducing things to see what happens. I'll be seeing the doc next week to test for thyroid function. I'm not really too set on 'proving' what helps me right now since I'd rather be healthy first. Being gluten- and fructose-free is my first goal.