Very interesting.... First thing I'd do is check the potential side effects of the drug you are taking and see if that symptom isn't actually listed right there.
If not, I did a google search and found a list of five medical explanations for cold hands that aren't simply exposure to cold. Most were diseases and seemed unlikely to be the cause, though one stood out - hypothyroidism. Maybe the medicine you are taking is affecting your thyroid?
I did a quick search after that for drug-induced hypothyroidism and found this:
Drug-induced hypothyroidism may be caused by:
Drugs used for hyperthyroidism (overactive thyroid), such as propylthiouracil (PTU), radioactive iodine, potassium iodide, and methimazole
Treatment with lithium or iodides in certain people
Unusual causes of drug-induced hypothyroidism include:
Eating a large amount of iodine-containing seaweed
Povidone iodine (Betadine)
Too much iodine may cause either hyperthyroidism or hypothyroidism. For example, iodine used by the mother during pregnancy (or as an antiseptic in the delivery room) can cause the fetus or newborn to develop goiter (enlarged thyroid gland). This can cause temporary hypothyroidism.
The most severe form of hypothyroidism is called myxedema coma. This is a medical emergency. Severe hypothyroidism, however, is rarely related to drugs.
Coarsening and thinning of hair
Decreased hearing ability
Puffy face, hands, and feet
Thickening of the skin
Thinning of eyebrows
Joint stiffness may also occur."
Though you might not have full blown hypothyroidism, this says even eating a lot of iodized salt could slow down your thyroid.