The reason Dot's tail is always braided is to keep it snow-white - and to keep its length from dragging on the ground behind him.
First of all, don't brush the tail. Ever. I was always told that every tail hair broken is $1 off the horse's price. So, touch it as little as possible. As long as there's no landscaping hanging out of it, just leave it alone. If you really feel the need to separate the hairs, use your fingers - and then a wide-tooth comb. Always comb from the bottom up, and take your time. If you hear snapping sounds, you're breaking hair.
For any colour horse, it really does help to braid and put up the tail. The top may still rub a little, but at least the lengths won't break. I have braided ridicoulously long tails using this method, and they stay in for MONTHS.
Shampoo well, making sure to scrub the skin of the dock, and use a LOT of conditioner. I've found that Fructis conditioner seems to work really well on horse hair. Use a good double-handful, and really work it through the tail, top to bottom, and into the hair roots on the dock. Leave it on for a good 5-10 minutes. Rinse very well, and let dry. Don't brush it. Once it's completely dry, saturate it with ShowSheen or any other silicone spray, and let it dry again. Once dry, carefully separate the hairs using your fingers and a wide-toothed comb, and braid it - braiding in a long piece of baling twine. I use the whole piece of twine, so that half goes into one section of the braid, and half goes in another. Just fold it in half, don't cut it - you want the twine to be continuous through the braid. You need a good foot or so of baling twine left at the bottom of two of the braid's sections. Secure the end with an elastic.
Fold the tail in half, and pull the end through the tail, just below the dock, from the front to the back (towards the horse). You'll now have a loop, with the end sticking out the back of it and pointing at the horse's butt. Now, pull the end, again, through the back of the loop so that it's in the inside of the loop - and then poke it through the bottom, so that the end of the tail is now sticking out of the bottom of the loop. Pull the loose baling twine through with it to the inside of the loop, but NOT through the bottom. You want just the "brush" of hair stuck through the bottom of the loop. Now, use those two loose ends of baling twine to criss-cross around the whole tail loop thing, at the same level as the twine knot. Just go around once or twice, just to secure the whole assembly.
Get 3 or 4 lengths of baling twine, about 3 ft long each, and use them to make your horse a 'fly swisher'. I just stick the lengths through a loop of baling twine near the bottom, pull them half-way through and tie them in a couple of knots. Nothing fancy, as long as it stays in. This is shown in the picture below. Now, get a roll of VetWrap or other self-stick bandage, and wrap the whole tail in it. Leave the 'swisher' out, but wrap the knots of the swisher and the rest of the tail - only up to the dock. Do not wrap the dock.
For a grey horse, use blue 'people' shampoo. It's a lot cheaper than horse shampoo. Something like Blue Fox or Shimmering Lights works great. After conditioning, use FanciFull leave-in rinse, by Roux. You can find this in the hair colour aisle of your pharmacy. You just squirt it in, and leave it. The shade is White Minx (or Ultra White Minx, if you can find it), and is intended for grey human hair. It takes the yellow tinge out of the hair.
Remember that white hair is unpigmented, and does not have any sun protection. If you put a white-coated horse out in the sun, the sun will 'scorch' the hair - making it look yellowish. The blue rinse will help a good deal.