There were several cemeteries in the Winchester/Frederick County area during and before 1859. The main one in Winchester is Mt. Hebron. It has a website: http://www.mthebroncemetery.org/index.html
You might also like to try the Handley Library in Winchester. They may be able to tell you what cemeteries were around at the time. Also, they have several volumes listing burials that were compiled by residents of the area.
A search of findagrave.com find a Margaret A Anderson b. 1813, d. 1843 buried in Brucetown United Methodist Church Cemetery in Clear Brook, Fredk. Co., VA.