Short hair has been a thing for a men in a majority of western cultures for a very, very long time. Now the times are changing and we can see that women have short hairs too and men tend to grow their hairs in some cases. Just I read somewhere that long hairs would be a disadvantage in case of wars, so men in max cases preferred short hairs.
In very cold regions, beards are more common where men might have been outdoors fishing in snow. In hot regions, men might have been outdoors in the brunt of the sun farming and carrying objects and would have wanted to cut it short to stay cool. Women might have been indoors in the shade and so their hair might have not have affected their internal body temperatures as greatly.
Now as the times are changing, We see greater balance between both genders.