What's the advantage of Fields over Corrals?
1 cavalry units gathers Food about 7 times faster than fully upgraded 5-man Fields. Or about 3.5 times as fast if you consider the cost of the animal.
If we scale that up:
20 cavalry units, 15 Corrals, Stockbreeding
-> 2000 Food, 1000 Wood + 1500 Wood + 100 Food
-> 2100 Food, 2500 Wood
70 civilians, 12 Farms, Iron Plow, Gather Training, Fertilizer
-> 3500 Food + 1200 Wood + 900 Wood, 600 Metal
-> 3500 Food, 2100 Wood, 600 Metal
So the Corral setup costs less overall resources, the units are trained faster, you save 50 pop, the buildings take almost the same time to be build, Corrals take up less space, cavalry is harder to raid than civilians, and you can slowly garrison cattle into Corrals and get an even bigger advantage.
Why should you use Fields instead?