Dear Ms. Middleton,
Thank you for posting your request on History Hub!
We searched the National Archives Catalog and located Compiled Service Records of Soldiers Who Served in the American Army During the Revolutionary War in the War Department Collection of Revolutionary War Records in the War Department Collection of Revolutionary War Records (Record Group 93) that may include records for soldiers whose units participated in the campaign. We also located Case Files of Pension and Bounty-Land Warrant Applications Based on Revolutionary War Service in the Records of the Department of Veterans Affairs (Record Group 15). Sometimes applications provide information about specific battles of campaigns in which the applicant participated. Portions of these two series have been digitized and can be viewed online through the Catalog. Of the pension applications already online, at least six have references to the Snow Campaign. We also located Revolutionary War Rolls in Record Group 93 that may have records of the units that participated in the campaign. The above listed records are in the custody of the National Archives at Washington, DC - Textual Reference (RDT1). Please contact RDT1 via email at firstname.lastname@example.org for more information.
We searched WorldCat and located a listing for the book The Patriots in the Snow Campaign 1775: First Land Battle of the American Revolution in South Carolina that is available through at least 5 libraries. We also searched online and located the Roster of South Carolina Patriots in the American Revolution that is available as a name searchable database via Ancestry. There may be a fee for this service, however Ancestry can be accessed for free at any National Archives location. Some libraries also provide access to their patrons.
We hope this information is helpful. Best of luck with your research!