If the letters are in a specific collection, you can for the first letter have something like "Clinton to Samuel Percival, 23 September, 1814 , UR-234, Box 5 Folder 19, DeWitt Clinton Papers, New York Public Library, New York, NY". The second time you cite that source, for a different letter, you can have less: " Clinton to John McKendree, 14 May 1834, DeWitt Clinton Papers, UR-432, Box 56, Folder 23". If the letters come from all different sources, though, yes, you need to spell it all out. You need to be telling somebody where they can look up the original letter.

Here'sa nice little website with the rules for citing archival stuff, with different examples for the different styles, be it Chicago, APA, etc.

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