Emmet attended St. Paul's School in Concord, New Hampshire and Columbia College. He studied law in the law office of Judge Martin K. Keogh and spent a year in Columbia Law School. He graduated from there in 1891 and was admitted to the bar in 1892. He initially practiced law in his native county, but in 1894 he formed a partnership in New York City. Almost immediately after his 21st birthday, he was elected Trustee of New Rochelle, serving in that position from 1891 to 1894. He was a delegate to the 1894 New York State Constitutional Convention. In 1900, Mayor Van Wyck appointed him to the New York City Board of Education. He was a delegate to the 1904 and 1912 Democratic National Conventions.