I have good luck with iodine shampoo or betadine scrub. I know it doesn't sound as if it should, but try it. It does tend to "strip" the hair, especially if used on manes and tails. so a conditioner is recommended
Pert Plus shampoo (the human kind!) or Head & Shoulders.
You know those show oxen at the fairs, the ones that are PURE WHITE, and cows always shit all over themselves...I asked a local lady how she did it, and she said "Pert Plus! It's been my go-to for YEARS!" I tried the Head and Shoulders on my mare with white socks, and the white was so bright it nearly blinded me in the sun!
"If you think nobody cares about you, try missing a couple payments..."