I have checked the Military History of NH 1623-1861 by Chandler Potter and in pt. 2 of that book there is an index to soldiers who served in the War of 1812. Unfortunately there is no entry for a Samuel Prince. Sorry to be the bearer of such news. You might try the History of Hillsborough Co., NH by D. Hurd for the section on the town of Hillsborough to see if it gives a list of soldiers.