Assuming Samuel was born about 1810 in Otsego Co., NY:
I found no Olmsteads in that county in 1810 census; however, in 1820 there are three:David, Horace, and Huram (Hiram??).All 3 have males in the household age 0-10, and David and Horace have males age 10-16.
Perhaps you could contact the county library in Otsego and/or the local historical society for information on these Olmsteads.
By the way, the correct spelling is "Burnet" county.