I have had a hot face etc from time to time and some sweating in (generally when the seasons change) over a number of years. The hot face doesn't bother me out in the fresh air but is very noticeable in the house.
I have never had the cold legs before but the seem to come and go with the varicose veins.
No. It can be in both legs but mainly in one. It is hardly noticeable when I am in bed and also seems to be improved by phisio on the calves. The "cold" legs I have had for a couple of months, the hot face a couple of weeks.