However, I've always been very cold natured and typically have blue nail beds all during the winter ever since I was very young.

That is either Raynaud's phenomena or Raynaud's syndrome.  Hypothyroidism is one cause of Raynaud's phenomena.

I tried the iodine therapy. That did not work. But it probably would not help hypothyroid condition anyway.

All depends on the cause of the hypothyroidism.  There are many causes of hypothyroidism.  And not all causes respond to iodine therapy.  And iodine therapy can aggravate Hashimoto's thyroidosis.

I have been trying to build up my adrenals by use of HV suggested herbs, and supplement with vitC and B50 daily. I'm not sure that is helping my cold condition.

My feet are already well chilled, and it is 77F in the house. I wonder if there is something I can specifically do to build up release of cortisol. I wonder if higher cortisol is even healthy. I never look forward to winter. I become a hermit and antisocial.

Again the Raynaud's is a side effect of hypothyroidism, but there are many causes.  Hypothalamic or pituitary dysfunction, chlorine, fluoride or bromine exposure, hormonal issues, adrenal dysfunction, poor T₄ to T₃ conversion, high rT₃, Hashimoto's, etc.  Not all will respond to iodine, and not all will respond to building the adrenals.