Yes there is an 1860 census. There was one every 10 years from 1790 though the 2000 census. The 1890 was mostly destroyed in a fire.The access to the US census is delayed 72 years so the 1930 census just became available this year.
When I go to a library (probably Dallas) I will check the 1860 index books.The 1870 was easy because it was on-line at the Heritage Quest site.The 1880 was easy because of the LDS 1880 census CD set.
I believe by the 1860's the California Gold Rush was over but there were several more gold and silver strikes in other states or territories later in the 19th century.