Yes it does make a major difference under the majority of the judges we see year in and year out. This last year I went against the adtage of not showing a cremello with a filly out of "Cherryville's Rio de Oro" our main stallion. She was very very good as far as conformation is concerned. Long neck, great head, straight legs and a great topline.
We had two fillies in her class and the other filly was a buckskin. Under a total of eight judges the buckskin which was not a better filly, won every time. I finally gave up and retired her to the breeding pen and No she is not for sale. LOL
We have a bunch of pinto horses in our herd and each year one of the things we pay close attention to is what Connie mentioned, where is the white and does it create an optical illusion of a short neck, short or long back, turned legs etc. etc. And yes we have had a colt that had a swirl of white on his legs in a place right above his hoof that when you looked at him made his very straight legs to appear to be turned. Needless to say he did not work in the show ring.
As far as app's are concerned, I also agree it is really hard to compete when you get the mottling around the mouth etc. You can overcome it some of the time, but it does make it harder.
Bottom line color does matter in some cases. But with all that said I still love to look at our pinto's and other colored horses. My indian horses as I call them. Who cares what the judges like, untill we are in the show ring. LOL