Some book titles to get you started. This is not an exhaustive list!
Letters from the promised land: Swedes in America, 1840-1914
Barton, H. Arnold, 1975.
America, reality & dream: the Freeman letters from America & Sweden, 1841-1862
Friman, Axel; Stephenson, George M; Barton, H. Arnold; 1996.
Norse immigrant letters: Glimpses of Norse Immigrant life in the Northwest in the fifties
Eide, Richard Benjamin, 1925.
Mom's letters home.
Larson, Anna Johnson, 1971.
Letters from Astrid: Swedish roots of an American family
Hanson, Carol Carpenter, 2013.
Land of the free: Bjørnstjerne Bjørnson's America letters, 1880-1881
Bjørnson, Bjørnstjerne; Haugen, Eva Lund; Haugen, Einar Ingvald; 1978.
Śami reindeer herders in Alaska: letters from America: originally published in Nuorttanaste 1901-1937
Kárášjohka : ČálliidLágádus, 2014.
With affection, Marten: a Swedish immigrant's letters about his struggles and triumphs homesteading on the prairie
Hofstrand, Richard K., 1983.
Up in the Rocky Mountains: writing the Swedish immigrant experience
Attebery, Jennifer Eastman, 2007.
A ring and a bundle of letters: an immigrant's story and the family's stories back home: with genealogical information on Eric Helsten's family
Voolich, Erica Dakin, 2013.
Swedish Annie, an immigrant life on the Iowa Prairie: love letters
Hartrman, Gerda Preston, 2005
In their own words: letters from Norwegian immigrants
Zempel, Solveig, 1990.