nose
The person with fever feels cold because his body inside is not heated because all the bosy heat is outside his body
you shiver and become cold dee dee dee
Your nose gets stuffed first
The wind blows your body heat away from you. And if the wind feels cold it probably is cold.
Your urine comes out at body temperature, which even if dangerously low, would not feel cold to the touch. If your pee feels cold to you it is because it is wet and just feels that way without actually being cold.
convection
Sometimes your body just feels cold sometimes and it could be a cold or a fever.
If you have the cold and/or a fever. your body feels cold, but it's your bodies defenses trying to cook out the bacteria that caused it in the first place.
the sweat cools you off but then you are wet and you may get too cold.
Hypothermia
Of course, do it all the time.
For example, you are touching something that feels like you are putting your hands into something very ice cold. That is how you can lose heat from your body.