Marten prime up earliest.They carry no body fat(unless they have been living at a carcass pile) and depend on fur to keep warm.Mustelids have a high metabolic rate and hunt for food constantly in winter.They have evolved thick insulating pelts as a result that come in early.
Animals with no fat and high metabolic rate generally prime up earlier and develop heavy insulating pelts.
Bear is a good example at the opposite end.
When they go into hibernation,their fur is short and not much for insulating quality,but they have a very thick layer of fat under the skin.(similar with beaver)As the winter progresses their fat layer shrinks considerably and the fur grows to take over the job of insulating the animal to hold body heat.
Bears are prime here when they come out of their den for a couple weeks end of may/begin june until they start to rub and shed.
When I hunted a lot of spring bear,I could tell by looking at the pelt what condition the animal was in.A lot of the larger bears had shorter fur and still retained an inch or so of fat under the hide.Their hides remained in nice shape longer than smaller bears in spring.
Smaller bears in spring often had thick wooly underfur and no fat whatsoever left under the hide,and were shedding and rubbing right away in spring.