In strict Army terms, the only woman authorized to travel with Civil War troops was the laundress. Regulations specified how she was appointed, how many there were, how she was paid, how much she was paid and how she fit into the overall organization. Read more about Civil War Army laundresses in this article:
The Second Minnesota Battery had an official laundress in 1862. Her name was Sylvia Townsend and she accompanied her husband when the Battery went south. Her biography can be found on the 1862 Roster page under the Historical section.
(NOTE: The Document is in PDF format)