Q:Why do some people feel extreme cold?

People show different sensitivities to low temperature because of variations in body mass, muscle mass, and genetics.

All humans on the planet are vulnerable to cold.   Because we are really bad at retaining heat in the cold.

One factor that dictates how well someone can tolerate low temperatures is their history to cold exposure. With time one can actually have some level of acclimation. For instance, people who move to colder climates tend to feel cold early on but are able to tolerate the extreme temperatures.

On a biological level, body mass is a major driver of cold tolerance in people. Those with a smaller body mass have a larger surface area relative to volume, so they tend to lose more heat from the surface of the body. If somebody's very small, they're going to exchange heat with cold temperatures much faster. If they're much bigger, it's going to take more time.

  People with a higher muscle mass also generate more heat through metabolic processes, potentially helping them better tolerate cooler temperatures. Muscle mass is actually your best protector when it comes to cold.

  However, some factors beyond body size also influence how sensitive people are to the cold. When you look at populations that live in Arctic conditions, they tend to be smaller, and they tend to have an average low body mass. How do people from these populations thrive in freezing conditions then? 

Scanning the genomes of Inuit people from Greenland revealed variants in genes involved in promoting heat-producing brown body cells.¹ A separate study in the same population indicated that some genes associated with adipose tissue differentiation and body-fat distribution are expressed differently, likely contributing to cold tolerance.²

Those who carry a mutation in a gene encoding the skeletal muscle protein alpha-actinin-3 maintain core body temperature better than those not carrying this mutation.³

Genetics could be related to blood flow also.  In cold conditions, blood vessels in the skin constrict, restricting blood flow to the extremities like fingers, toes, and the nose. While people may feel colder due to this constriction, it helps maintain the core body temperature. Genetic variants in genes encoding a collagen sub-unit and a hormone receptor are linked to the regulation of blood flow in response to cold.⁴

So  everybody feels the cold biting differently depending on the factors that affect them.