Blizzard was born in Saltville in 1919. She has Apache and Irish ancestry. When she was little, she and her family moved to Plum Creek. Her mother taught Blizzard and her sister how to create art using a pit-fire method. During the Great Depression, she left school in order to be part of the National Youth Administration. She worked in a munitions factory in Bristol during World War II and after that, worked at a textile mill in Chilhowie until 1958. Blizzard had contracted black lung and lost one of her lungs. Her husband was crippled in an accident in a coal mine and eventually their marriage failed. Her husband died in 1954. Blizzard developed paranoid schizophrenia after these events and her art helped her deal with visions she saw and the feelings she needed to work through.

She began making art for sale in the late 1950s and sold her pottery in her daughter, Mary's, store. In the early 1980s, her neighbor, Michael Martin, contacted a friend to take some of Blizzard's work to a gallery in Buckhead run by Judith Alexander where Jonathan Williams discovered her work.