One short term adaptation that human bodies use to fight cold is usually triggered as soon as you feel the effects. Shivering is a bodily reflex used to maintain homeostasis and prevent hypothermia. Muscles throughout our body begin to shake, expending energy and creating warmth. This adaptation starts at the soonest inclination of lowered body temperature and usually dissipates as soon as your core temperature regulates to normal.
One facultative adaptation that humans use against the cold is the process of vasoconstriction, which is the narrowing of blood vessels near the surface of the skin. By doing so, the body preserves body heat by slowing down blood flow, which causes the skin to cool down, but allows less heat loss. This however needs to be monitored as the colder the environment gets, the more susceptible you are to frostbite. The body does have a check for that in vasodilation, which increases warm blood flow, thus preventing frostbite. The body switches between the two for as long as it is needed.
A developmental response to cold that humans have acquired is the shapes of our bodies. One of the many factors that attribute to body shape, colder environments typically found north of the equator have necessitated the need for stouter, bulkier bodies which allow them higher heat production. Joel Allen's findings also tell us that bodies in colder environments tend to have shorter appendages in order to have less body surface area. These bodies are a long-term effect of living in the cold and do not change with the weather, they are permanent in some form for life.
Probably the biggest cultural adaptation humans developed against the cold comes from the use of clothing. For example the clothing made by the Yup'ik people of Alaska are one of the most effective cold weather clothing around. They made waterproof outerwear using the intestines of sea mammals, and used animal hide and fur to make clothes and footwear. They even used grass to make insulating socks.These inventions greatly improved their survival in the cold harsh environment of Alaska without using much or any modern technology.
It is always beneficial to study human variation caused by environmental clines. It allows us to develop a complete understanding of how our bodies react to these different environments, for both its positives and negatives. An example of this is using hypothermia as a therapeutic method for victims of cardiac arrest or acute spinal or lung injuries. Without our extensive knowledge of how cold weather affects the human body, we wouldn't be able to explore and exploit the benefits of what is usually considered a danger.
I wouldn't be able to use race to understand the adaptations as it has no correlation to these changes. Our bodies have a distinct connection with the weather and thus develop safety nets to avoid injury or death. You'll see these changes in all humans. Race has zero involvement in deciding whether or not a person can shiver to regulate homeostasis. Or whether your family develops stout stocky bodies (as we see this in both Inuit tribes and Europeans who live further away from the equator.) Race is 100% a societal construct and should not be used to study human variation. If anything, these variations are a key component to how humans see "race", which is just a categorization of visible phenotypes and stereotypical characteristics.