Norma Dobler was born Norma Woodhouse on May 2, 1917 to Lester and Bessie Woodhouse in Haines, Oregon. The family moved to a farm in southern Idaho's Canyon County during the fall of 1917. Norma graduated from Caldwell High School in 1934. She then attended Links Business College in Boise for a year, the University of Cincinnati for two years and graduated from the University of Idaho with a degree in Business in 1939. Upon graduation, she worked in the University of Idaho registrar's office for two years.

Norma married Clifford Dobler on June 14, 1941. That year Clifford joined the faculty of the University of Idaho as an associate professor of political science where he taught business law courses for the next 36 years. After her marriage, Norma devoted herself to raising their three children and became very active in volunteer work. She served for 12 years as Sunday school superintendent for the Methodist Church, 12 years as a 4-H youth leader, and worked with the Campfire group for two years. She also worked as a county fair judge and election judge. Dobler spent six years on the Moscow School Board and three years as president of the Idaho League of Women Voters before her legislative stint and served nine years on the Idaho Tax Board of Appeals afterwards. She took up her career again in 1971 and worked as secretary to the State Extension Forester until 1975. She was awarded life membership in the PTA, American Association of University Women, United Methodist Women, and Delta Kappa Gamma Education Honorary and received the "Citizen of the Year" award from the National Association of Social Workers. She is listed in several "Who's Who" books, and "Two Thousand Women of Achievement" and the "Dictionary of International Biographies".

A staunch democrat, Dobler was long active in politics through her work with the League of Women Voters. In 1973 she won a seat in the state House of Representatives. During her four years as a representative, she served on the Education, Health and Welfare and Resource and Conservation committees. In 1977 she was elected to the state senate, serving for five terms until her retirement in 1986. Her committees included Health, Education and Welfare, Resources and Environment, Judiciary and Rules, and State Affairs.

Dobler was a passionate crusader for the rights of women, senior citizens and children, education and the environment. Legislation that she sponsored, or was particularly involved with, concerned displaced homemakers, Idaho's ratification of the Equal Rights Amendment, day care licensing, reapportionment of the legislative districts, abortion, divorce, drinking age, driving under the influence of alcohol, harassment (hate crimes), higher education, liquor revenue, and the state liquor dispensary system. She was also active on the Development Disabilities Council, the State Employment and Training Advisory Council, and the Idaho Cancer Coordinating Committee. On a national level, Dobler served on the Education Committee of the National Conference of State Legislatures, the advisory board for the National Education Data Library, the American Association of Retired Persons' legislative committee, and a national commission to prevent telemarketing fraud of senior citizens.

Norma Dobler passed away on June 1, 1998 from head injuries she suffered in a fall at her Moscow home. Her husband; her children, Sharon Vega, Terry Dobler and Carol Harris; a brother, Clyde Woodhouse; 11 grandchildren; and three great-grandchildren survived her. Upon her death, Senator Marguerite McLaughlin commented, "She probably was the most fair legislator I ever knew. She listened to both sides and tried to make decisions based on that."