Horse crazy? Go there!
My sister and I (both horse nuts and former horse owners of advancing age) visited the museum after seeing a performance at the Spanish Riding Academy, where the Lipizzaners perform.
The museum is not that spectacular, although very interesting for those who know their tack and training methods.
The star attraction, though, is in the little video room in the basement, where you can watch the best Lipazzaner performances on film (as many times as you want to, if you're not in a hurry). These films are quite awesome.
If you love these horses, don't miss the stud farm at Piber (near Graz), where you can get up close and personal with the horses to an extent that would never be allowed in the U.S. for fear of theoretical liability.
If you search for Lipizzaner - Piber or stud farm Piber, you should find their excellent web site.