You have everything for basic cleaning, but if you want to do heavy-duty cleaning you'll need a few more things.
You will need a rag though, to polish the coat to a shine. A rag is also good for cleaning around the eyes and nose.
You might want to pick up a mane-comb, one of those little ones just for pulling the mane. You can't braid an un-pulled mane so braiding bands are useless without a mane comb.
You will also really need a shedding blade for the winter/spring, otherwise a winter coat is impossible to get off. A curry comb is nothing compared to a shedding blade!
My horse really likes those jelly-type curry combs which massage the horse at the same time as they're groomed.
