To extend Twelfth's answer... a few things off the top of my head in no particular order. Most of these apply to lower technology human societies where modern technology hasn't compensated for biological differences.
Humans lack fur because we hunt by running. Humans can out run any animal on earth.
It's people without horses catch horses. They jog after horses, never catching them but never letting them rest either. After about 20-25 miles at most, the horse can't run any further, the human walks up and puts a rope arounds it's neck.
With flint, wood and bone weapons, hunters wound prey and then run it into the ground.
It's hard to cool by sweat with fur. If you ever seen a horse, "lather up" you've seen the basic problem. Horses have very thin, fine, close knapped fur yet still it interferes significantly with evaporation.
So, first off, humans with fur would have evolved to hunt differently. Likely, we would hunt with traps or with in larger groups like wolves. In either case our entire physiology might shift. We'd be adapted to sprint horses or wolves, to catch game quickly.
One affect might be a decrease in sexual dimorphism (overt differences in body shape by sex.) Part of the difference between men and women can be attributed to men being more adapted to protracted exercise. Distribution in muscles, muscle recover time, more sweat glands etc all point to optimization of men for running. If such optimization were not needed, then men and women might be more similar in physiology just like wolves and other canines and just like wolves, there would be less specialize of labor and less specialization in behaviors.
Most sexually monomorphic species are matriarchal, with the entire group supporting the reproduction of the matriarch, at least in hard times. Human society might be radically different historically although we might start out with something like we have now after technology has leveled the playing field between men and women.
We likely would have had trouble with prolonged relative work like most pre-industrial agricultural work. Humans have to be careful not to kill horses and oxen by forcing the animals to work as long as humans do. We would adapt society to allow working in sprint shifts, with two or more individuals tag teaming a single job to keep the work going. If men and women where physiologically similar, they could swap off child care and work for everything except nursing.
Individuals might commonly pair up with siblings, other relations or friends for life, both specializing in the same job and together forming a complete work team. So, if someone was a blacksmith, their partner would be as well. People didn't have time to waste so individuals would have some secondary task to occupy them at a lower level of effort while they rested from the main task. Human social structure would be based on this partnership. It would affect everything from military units to marriage.
Humans would be less mobile in general, at least preindustrial. Unable to walk, march or run as far, they would have to adapt activities to being closer to home. Any systems based on walking, like cities, would be more compact.
Armies would march and move slower but move faster in battle itself owing to likely greater sprinting speed. Battles would have to be decided faster before exhaustion set in. Battles would be very intense but short. This would favor more organized forms of shock warfare, like Greek Hoplites. The idea would be to hit the enemy hard and fast and do maximum damage in the shortest amount of time. Alternatively, there would be more pressure to develop a rotational system like the Romans used to grind away at an enemy while preventing exhaustion of individuals.
If the pair system did evolve, that would be part of the military as well and if men and women were more physiologically similar, then women would participate in combat more. If women could fight, that would increase per capita fighters in the population. Combined with intense shock warfare, battles could be more devastating with more adults overall in a population likely to be killed.
Slavery might be more difficult both in terms of the danger of going to war to capture slaves, the added difficulty in controlling women and the inability to substitute humans for animals and machines in many circumstance e.g. treadmills. Managing slave work would be more difficult if slaves had to constantly swap out task.
Having fewer slaves would likely reduce the profitability of war (slavery being a huge driver of warfare in classical times.) It would also foster technological development because it would be difficult to solve a complex problem just by throwing more slave at it e.g. threshing grain or grinding flour.
There would be greater pressure to domesticate animals for transportation and labor and greater pressure to develop vehicles and machines. Riding animals and carts would be more common of basic necessity which would make it harder to restrict horses to military caste aristocrats. With less of mobility advantage, such societies would be less hierarchal and more egalitarian e.g. classical Greece with few mounted warriors relative democracy as compared medieval Europe with knights on horses like tanks and most of the population serfs.
Lastly instead of skin color, fur length would likely distinguish whether individuals had equatorial or polar ancestry. Equatorial peoples would evolve shorter fur while polar peoples would evolve longer. Fur color would likely be seasonal. In Equatorial regions, long fur might become a status marker indicating an individual did not have to labor and worry about heat. In polar regions, the opposite would occur, short fur indicating a individual had surplus wealth for heat or clothes.