Greene was born in San Rafael, California. She graduated from East High School and earned her B.A. from the University of Utah in 1980. She received her law degree from Brigham Young University in 1983.

She worked as a lawyer for software company Novell and then at a Salt Lake City law firm. She was deputy chief of staff for Governor Norman H. Bangerter.

As a young Republican, Enid met Joe Waldholtz and they were soon in a relationship. Greene ran for the House of Representatives in 1992 against Karen Shepherd for the Utah Second District, which was entirely contained in Salt Lake County at that time, losing by four percentage points.

Greene married Waldholtz in 1993. After her marriage, Greene took the name Enid Greene Waldholtz. During her 1994 rematch against Shepherd, Joe acted as her campaign manager and over two million dollars was spent. Greene was swept into the 104th Congress in the Republican landslide in November. She was named to the House Rules Committee, the first freshman on that committee in over 80 years. In March 1995, she announced she was pregnant. Greene became the second representative to ever give birth while in office (the first being Yvonne Brathwaite Burke) and the first Republican.

Her term was marred with scandal as her campaign was accused of campaign finance violations. Joe had borrowed money from Greene's father and embezzled funds from his own relatives. Joe Waldholtz disappeared in November 1995 and then surrendered to police. Enid announced that she was changing her name back to 'Enid Greene' and getting custody of her daughter. Greene held a marathon five-hour press conference that destroyed her Congressional career. Under pressure from Utah Republicans, she announced on March 5, 1996 that she would not seek re-election to Congress.

Greene was a candidate for Lieutenant Governor of Utah in 2004, but her ticket with gubernatorial candidate Nolan Karras was unsuccessful.