Dear Alex; I have never researched it, but you might want to check names from Smith and Henderson County Texas. There was a Norwegian Settlement south of present day Brownsboro, Texas, in Henderson county, and one of the crossings on the Neches river between Smith and Henderson Counties was referred to as the "Norwegian Crossing." A quick check of names in the Soldiers and sailors system shows, E, [Eliff] T. [Thomas] and J.J. Albertson, all brothers who were sons of a Norwegian family that emigrated to Tyler, Smith County, Texas in the 1850s. They show as being in the 11th Texas. Check Ken Jones web page on Texas in the civil war at http://www.tarleton.edu/~kjones/ He lists by county, what regiments had companies from that county. A quick check of the 1860 census at the Henderson County Texas GEnweb page shows a number of Norwegian born people. Their web site is at http://www.rootsweb.com/~txhender/txhender.htm
You might simply enter in obvious Scandinavian names in the Soldiers and Sailors system at http://www.itd.nps.gov/cwss/ and see what you get.
Happy hunting. The Smith County GenWeb site is at http://www.rootsweb.com/~txsmith/ You are fortuneate in that both the Smith and Henderson county Genweb pages have both the 1850 and 1860 census on line. Let me know how many you find.