Tack shops have whitening shampoos like Quicksilver. A cheaper option that works well is Jirmack human shampoo for white hair and that can be found at walmart or a place like that. They say you can use laundry detergent but its not for living things so Ive never tried it...
For the tail we have always used Apple Cider Vinegar. It breaks down the dirt in the tail and and helps whiten it, especially if it is fairly dirty. We also tried normal vinegar but it didnt work as well. This only works if you have a horse that you can trust fairly well.
What we did was first rinse the tail to get the surface dirt out. Then we put warm water in a bucket and added some vinegar. Put the tail in the vinegar water solution and hold the bucket up as far as you can, including as much of the hair around the dock as possible. Then hold it there for 5 minutes or so. You will see the vinegar water start to get very dirty, and thats when you know to dump the bucket. You may have to repeat this a few times, depending on how dirty the tail was. At the end the vinegar water should stay fairly clean. Then when you are done wash the tail as you would per usual. If you want it super white you can use the whitening shampoos listed above. This method works on all tails, not just white ones. My horse has a black and very light colored tail and it got all of it very clean.
I dont think this would work for the mane because you wouldnt be able to keep the mane in the shampoo.
My friend used baking powder I believe on her horse to cover up spots that wouldnt come out all the way.
so it may be a little late but my mom and i have also used cheapo whitening toothpaste believe it or not. you will need to use it a few time and be generous with it, the only problem that we have experienced is that my mare thinks that the toothpaste is a mint for her lol
Whatever you use don't use more than the recommended amounts or the time it sets before rinsing out. A gal left her whitener in too long, which she admitted as a warning to others, and the horse wound up with a purple tail. Apparently the stuff wouldn't shampoo out either, at least not right away.