The reason for that is because shampoo strips out the natural oils from the skin and coat, and even heavy conditioners and lots of currying can't give that back. I try to use more natural shampoos as they tend to not have extra harsh chemicals. I particularly like EQ Solutions. Occasionally I will use colour specific shampoos mixed in, especially for a show. I would definitely advise a whitening shampoo on socks and stockings, letting it sit for about a few minutes before rinsing (but not too long, no blue socks!).
A lot of what I would say has already been said, though, about how a good coat comes from inside out. Be sure your horse is eating well and getting the proper nutrition. With that, supplements can also be added. Grand Coat is a nice one. I've had the best and most financially reasonable luck with adding about a teaspoon of ground flax seed in the feed. It really does make an enormous difference. I also curry the heck out of my horses, I spend hours grooming them when I can.
Between those things, people at the barn always marvel over my horses and ask me what coat shine I'm putting on them to make them glimmer like that. Fact is, I don't put a thing on 'em, I just practice what I'm preaching.