When and why did the color orange (and yellow and 'red') become associated with Buddhism?
The oldest Buddhist robe color we know of is yellow/orange. The original monks made their robes from discarded cloth found in rubbish and on cremation grounds. After washing, the robe-cloth was boiled with vegetable matter—leaves, roots and flowers—and often spices, which would turn the cloth some shade of orange. Hence the name, "saffron robe." 

The tradition stuck and yellow/orange is now the color of choice for Theravada Buddhists in Southeast Asia, as opposed to a maroon color for Chinese and Tibetan monks. This has various reasons: first, the climate is very different,so the natural dyes of South-East Asia are not found in Tibet. The harsher climate also means that the traditional triple robe would offer little protection from the elements. The second reason is traditional robes expose the arms and shoulders, which was deemed unseeming in Chinese culture. So monks began to wear a long robe with sleeves that fastened in the front, similar to robes worn by Taoist scholars. The robes worn by Tibetan monks are derived from a mixture of the clothing "rules" from the traditional robes and Tibetan &amp; Chinese "dress code".

Japanese and Korean Buddhist monks also wear robes styled after the clothing traditions of their culture. In Japanese culture, red is associated with power and blood, and yellow is associated with nature. Shinto priests predominantly wear black, so this became the most common color for Buddhist robes in Japan.