Green’s Dictionary of Slang

(US) an over-dressed, upper-class individual, thus phr. dressed up like a plush horse, also attrib; a style of dressing identified as the property of social conservatives.

1910		Ogden Standard (UT) 15 May 22/4: She’s a real woman then, not a plush horse.
1919		West Virginian (Fairmont, VA) 28 July 7: Her homely daughtrer is all dressed up like a plush horse and nowhere to go.
1922		South Bend News-Times (IN) 6 Apr. 19/2: The plush horse era in men’s clothes is over [...] The conservatives are again in power.
1932		(con. 1919) Dos Passos Nineteen Nineteen in USA (1966) 677: I’m with the worst old set of plush horses.
1936		(con. 1920s) Dos Passos Big Money in USA (1966) 790: It looks so silly to see a girl dressed up like a plush horse with a man in a business suit.