Short answer? Cheddar Cheese is orange because they color it as such. But that’s such a dull answer and still doesn’t explain why they color Cheddar that color.
So here’s the cool answer: Milk takes on different colors based off of diet of the animal. Thus, a diet of beta-carotine will result in orange-tinted milk and thus, orange tinted cheese. This is the fact you need to keep in mind for the following hypothesis:
Cheese taste is also highly affected by the food an animal eats. If a cow eats a lot of onions, its milk will lead to oniony cheese.
So back in the day in England, Cheddar Cheese (that is to say, cheese from Cheddar, England) was found to be quite tasty indeed – better than most other English cheeses. As it was so popular, the folks in Cheddar could charge a wee bit more for their cheese than other folks.
Then some scalawag noted that there was an orange tint to the Cheddar cheese. Being a greedy little bastard, this scalawag added a tad bit of coloring to his own cheese, and started selling his cheese as Cheddar as well. People’s tastes being what they are, they probably equated “more orange” as meaning “more Cheddar-like”, and started paying more for the more orange cheeses.
Meanwhile, back in Cheddar, they couldn’t understand why people went ga-ga over orange, as the color had absolutely nothing to do with the taste. The taste came from the fact that their cows ate different grasses and that the cheese were aged in different storage facilities than other cheese making areas of Britain.
That’s why Cheddar Cheese is orange. Because we want it to be.