Yeah, whatever you do don't aspire to be as limited a pianist as Horowitz!
Why do you think he was limited? He actually excelled in a number of different styles. He played wonderful Scarlatti. His classics--Haydn, Mozart and early Beethoven were superb (well, at least before he started adding to them odd manerisms). I don't even mention romantics, but he was also pioneering some newer and modern music like Scriabin, Prokofiev (6-7-8 Sonatas), Barber, and even Poulenc and Kabalevsky. Definitely he was not at his best in such monuments like Schubert B flat major Sonata, Brahms 2nd Concerto, or Beethoven Op.101, but nevertherless, he was equaly good in miniatures and big forms.
On the other hand, ANY pianist has limitations. Even for such titans of keyboard as Gilels or Richter there were whole layers of repertoire where they felt just helpless and I believe Horowitz in this respect was not more limited than they were.
In any case, out of all romantic pianists Horowitz in fact, seemed to be the most versatile.
Best, M