Your John Anderson Simpson (age 39, Tennessee, farmer) is indeed in Mt Vernon, Lawrence Co, Missouri in the 1860 census Family number 1275 pg 202 of the Mt Vernon Lawrence county census record. He is listed with wife, Margaret (35, TN) James A (13,TN), Nancy A (12,TN), Sarah F (10,TN), Martha C (7, MO), Joel N. (5/12, MO) This indicates the family located to Missouri between 1850 and 1853.

He is listed as a First Lt. Company B, Ford's Battalion Missouri Cavalry, per NPS records.

He has a pension application filed by his daughter Nancy A Simpson with one William A Skaggs as her guardian with his death listed as Jan 17, 1865. This would be indicative of his wife passing before he did and indeed I cannot find an appropriate Maragaret Simpson in the 1870 census listings. The pension was allowed in March 1876. He is listed as having served with the 7th Mo Cavalry (Union) on this pension index card. Pension numbers are 52435 filed with Missouri 1865 and 175172 as minor child pension with Arkansas. There is a Missouri Service Record of a Private J A Simpson 7th Mo Cav Company M died Dec 11, 1864 buried Little Rock National Cemetery.

Thus a bit of confusion, though perhaps not, as many men ended up serving both sides during the war. I can not confirm that we are not talking about 2 different John A Simpsons each with a daughter Nancy but it gets a little thin.

The 1850 Census has the young family in District 4 Bradys Rock, Cannon Co., TN by the way.
Joel V Simpson ends up in Spring River, Lawrence Co, Arkansas Married in 1881 to a Sarah J.

So let me know where I'm going wrong and I'll see if I can fleash this out a bit more with some better source documentation.

John R