The 1900 census is the earliest census in which you will find an immigration date but you can estimate the year by the age of his first U.S.-born child, in the 1870 census.
1870 Bountiful, Davis, UT, FROST household:
Allen 30 England, Anna 28 England, Alice J. 1 UT, Harrison 4 UT, Allen 6 UT.
In the 1900 census he is in Snowflake, Navajo, Arizona Territory and he said he immigrated in 1852.