In the days when horses were much used for carrying burdens no their backs, the animals that gave the least trouble were given more work to do than those which were stubborn or intractable. Today a willing horses is a person who is so good-natured and helpful that everyone takes advantage of him.
The proverb comes from a poem by the English poet John Gay, written in 1716. The full verse reads:
All lay their loads on the willing horse
Not he that draws, but he that bore.
The poem was later adapted into a popular proverb, which is now widely used to refer to the tendency of people to take advantage of those who are willing to work hard and help out.