Folk influence is heavy in Brahms' Hungarian Dances. And I love all the rest of Brahms.
I was raised on Mozart, probably spent a lot of the 9 natal months with him, too.
When I hear the term 'classical' I lump in the romantics as well, which for me is the Slavs (Tchaikovsky, Borodin, Gliere, just look up the poem/ song "Russian Composers" by Ira Gershwin), Dvorak, Smetana, Enesco (Romanian really), and one of my faves, the Armenian Khachaturian, who has Alaska relatives.

And while he's usually left out of the ranks of the great, I always make it a point to bring up Nikolai Andreyevich Rimsky-Korsakov who gave us so many memorable vignettes and orchestrated many works by others, and orchestration counts fully as much as composing in my book.