Greenwood first visited Woodstock as a child in 1920. At the age of fourteen, she began her studies at the Art Students League under George Bridgman, Frank Vincent Dumond and John Sloan. It was during the same year that she held her first exhibition at the Woodstock Artists Association. In 1932 Greenwood spent time in Taxco, Mexico and her work gained the admiration of the Mexican muralists, Diego Reivera and Jose Clemente Orozco. This led to a commission from the Mexican government to execute a mural on Tarascan Indian life. Greenwood, at the age of twenty-three, thus became the first woman to receive a mural commission from a foreign government. Greenwood is best known for her ability to portray in her work the human diveristy she observerd throughout her travels.