I am someone who always feels very cold. No medical reason, I think it's just because I am quite small and thin with little fat for insulation.
When I am at home I always have the thermostat set at 21-22, and even then often find myself sitting next to a radiator or electric heater.
When I go to friends I always find it very cold. I have a choice of either leaving my coat on, or mentioning that its a bit chilly in the hope that they will say they are cold too, and turn on/up the heating. I feel that whichever option I choose comes across as rude as I am implying that their house is cold (sometimes it genuinely is but most of the time it's just me)
Which would you find less/more offensive? Someone not wanting to take off their coat in your home? Or someone you to turn on/up the heating?