I don't know that they are not being maintained and I think one is always safe in assuming the handlers, riders and stable staff are at the very top of their game. I do see the horses on parade and standing guard in the UK, and parade Palominos. I think we can do better and we can do more.
For fun look up the history of the Old Guard stables at Arlington, and the change from donated horses to the beautiful animals and conditions they live under today. We should have the best animals, care and turnout in the world.

For the upcoming parade, the military units might be able to borrow some city police horses. They are trained and conditioned to deal with something like a parade and will do fine as long as their riders are competent.