Find food
Foxes and wolves grow thicker fur, polar bears too and seals and walruses have alot of fat
A fox can grow fur that gets thicker as the season gets colder.
The actuall patern would not change, but in winter it would have a thick coat, autumn losing the coat, summer normal coat (thin), spring, begining to grow the thicker coat again.
It is a simple natural response to keep themselves warm.
Shaving does not "make your hair grow back thicker".
No, they do not grow back thicker. There is a bit of a fallacy regarding this, but it has to do with the hair loosing the normal taper and being cut off square at the end, so it may appear thicker, but the thickness of the hair does not change.
nothing
I'm not really sure I understand what your question means, did you mean why or how? I'll take a guess at a general answer. Winter affects all animals by the cold weather, but native animals are adapted to it, so they grow thicker coats of fur or fatten up for winter to hibernate. Foxes don't hibernate, so they are one that grows thicker fur. More important effect is how the weather changes what foods are available. Lack of food, not temperature, is what sends most migratory animals south. Animals like foxes are predators that don't migrate and they eat mostly rodents and rabbits. Some rodents hibernate in the winter, so they are harder for foxes to find and deep snow might make hunting more difficult.
No, thinning your hair does not make it grow back thicker. When hair is cut or thinned, it may appear thicker at first due to the blunt ends of the remaining hair, but the individual strands themselves do not change in thickness. Hair growth is determined by genetics and other factors, not by cutting or thinning techniques.
Eat more.
Yes, fennec foxes do shed their fur, typically during seasonal changes, particularly in spring and fall. Shedding helps them adapt to temperature fluctuations in their desert habitat by allowing them to grow a thicker coat for winter and a lighter coat for the heat of summer. This process is essential for their thermoregulation and overall health.
Nothing that you can put on from the outside will make your hair grow thicker. (With the possible exception of Minoxidil.)