Hi, many thanks for the query!
This is the classical history of "Peripheral Vascular Disease", if you are smoking or chewing tobacco further confirms the diagnosis.
Check with your doctor- "ankle brachial pressure index", if abnormal (more likely to be abnormal in your case) then
Do "colour doppler of both arterial & venous system" of the affected (cold) limb.
Check your blood pressure, blood sugar level, blood lipid profile
Treatment includes- First stop smoking/taking tobacco in any form.
Management of Diabetes
if you are having it, anti-platelet drugs with your doctor's opinion.
Do regular exercise.
Wish you a good health. Take care.