Many pianists who want to improvise classical music go about it backwards. (By this I mean "ineffectively.")
Instead of analyzing Mozart and then trying to improvise in his style, learn to improvise first, and then it'll be easy to improvise like him.
By learning how to improvise first, you'll begin to view written music in a new way. Then when you look at a Mozart Theme and Variations for example, you'll now understand what he did and you can try to play in a similar way to any given variation of his.
It's fun to take, say, a folk song, and use a left hand arpeggiated pattern similar to the one Mozart uses in one of his variations on "Twinkle, Twinkle Little Star." Or use an Alberti bass pattern like he does in his famous C major Sonata.
In general, you'll go much farther if you become comfortable improvising first, and then look at the details of Mozart's music. Not the other way around.
Above all, have fun and "let the music flow!"