I'm finding it absolutely amazing how well Walt Disney knew the field of animation. This letter could have been written last month with no modifications and still have been as applicable to animators as it was in 1935.
Disney, and a few artists under his direction, more or less created the system and criteria used to create and judge animation; at least in the USA, from a professional standpoint. Anyone in the west who is taught "animation principles" is taught material developed pretty much as ordered in this letter. What was known as "Disney Animation" and later "Hollywood Animation" was developed to Disney's specification and taste. (Despite what many think, Disney _was_ an animator, just not a very good one. However few would argue that he was a fantastic producer and aesthete.)
Now...
There _are_ other systems and "principles" and methods of staging for animation that are _very_ different from the ones Disney helped to develop. Some of them use some of the same tools developed by Disney Studios and their followers, but take them in very different directions. This is particularly true to animators working in countries other than the USA. (Take a look at films from Russia and the former Easter Block countries for some interesting counter examples. Or hell, at some of the fantastic stuff coming out of Japan these days.)
When I see a Pixar movie I see animators using "Disney" techniques as applied to the new medium; Disney is very much in their DNA. I'm still looking for the 3D animators to grow a set of principles for designed 3D, as opposed to those developed for "pencil" drawings.