Butter discolours for the same reason that apples or bananas turn dark – oxidation. And although better doesn’t have a peel to protect it from the ravages of air, it does have a wrapper surrounding it until it is first used. Only after the wrapper is eliminated or loosened does the butter darken.
Why does it get harder?
The cold temperature in the refrigerator causes the moisture in the butter to evaporate. Many other foods, such as peanut butter, become less plastic when refrigerated because of evaporation of liquid.