In the baroque, classical, and romantic periods, how did popular "low culture" music influence the classical music produced during those periods? Were influences more frequently from previous classical composers? Were the modernists (Bartok, Stravinsky, etc) the first to pull material from "peasant tunes" and other popular music of the day?
The Baroque and Classical 'Suites' and later 'Symphonies' (also other forms) can be considered as having grown from collections of dance-form pieces. Minuet, Courante, Allamande, Gigue... Even when Sonata Form came to dominate symphonic writing (for the first movement at least) one of the middle movements might still be dance-based, typically a fast waltz.
Popular melodies were incorporated in 'art music' long before Bartok and Stravinsky. A classic example is Mozart's 'Variations on “Ah, Vous Dirai Je Maman”' But it certainly happened much more often as musical 'Nationalism' accompanied a wave of political nationalism in the early 18th century. Mozart wasn't trying to make a political point. Jan Paderewski surely was - as well as being a pianist and composer he campaigned for the independence of Poland and, when it was achieved, served as its Prime Minister.
Tons of "classical" pieces either openly are based on folk songs, traditional themes and rhythms, or just work them in semi-clandestinely. Famous examples include Dvorak's New World, Mendelssohn's Scottish, Smetana's Ma Vlast (people only know the Moldau movement).