We took our baby last year and I nursed at various places throughout the parks. I fully intended to use those infamous baby stations, but they were never close by when I needed them, so I never even went in a single one of them. Honestly, if you're discreet, most people won't even notice, and if they do, won't care. If you're comfortable nursing in other public places (restaurants, etc.), than Disney won't be a problem.
One tip - I often went into a show or longer dark ride so I could be in the a/c while nursing. Depending on when you're going, sitting on a bench, holding a baby, and wearing a nursing cover could get really hot! Ideas - Hall of Presidents, Enchanted Tiki Room, Mickey's Philharmagic, Voyage of the Little Mermaid, Festival of the Lion King, Finding Nemo Musical, movie in France at world showcase, etc.