Snyder was born in Louisville and attended public schools there, graduating from duPont Manual High School. Snyder studied at the University of Louisville and graduated from the Jefferson School of Law. He began a career as a lawyer in Louisville in 1950. Snyder was elected as magistrate for the first district of Jefferson County in 1957 and was re-elected in 1961. Snyder also had business interests in farming, real estate, insurance and construction.

Snyder was elected to the United States House of Representatives from Kentucky's 3rd Congressional District, based in Louisville, in 1962. He was one of the few Republicans to vote against the Civil Rights Act of 1964. He was unseated in 1964 after only one term by former Louisville mayor Charlie Farnsley amid the gigantic Democratic landslide of that year.

Snyder then moved to Oldham County, which was in the neighboring 4th District, and immediately prepared for a run against 11-term incumbent Frank Chelf in 1966 The 4th was rapidly trending Republican due to an influx of new residents from Cincinnati. He took full advantage of this trend, defeating Chelf by almost eight points. He was reelected nine more times. In 1984 Democrat Pat Mulloy ran a surprisingly strong campaign and almost unseated Snyder; only Ronald Reagan's gigantic landslide win in Kentucky (by almost 20 points) kept Snyder in office. Rather than face Mulloy again, Snyder chose not to seek re-election in 1986.

The portion of I-265 in Kentucky is named for Gene Snyder, as is the federal courthouse building in Louisville.