From the book "City of Hudson Burying Grounds Interments 1829-1873" by Arthur C.M. Kelly, Kinship, Rhinebeck, NY, 1986 on page 173:
HORTON, Eliza, died Hudson, consumption, married, age 34 y.

In the 19 July 1870 Census at Hudson, Ward 4, Dwelling 168, family 207 living in the household of Sarah Suffman:
William Horton, age 45, male, white, Sexton Ep. Church, born England.
William Jr., age 10, male, white, born Ireland.
In the Hudson Orphan Asylum, 25 July 1870 Census, Ward 4, page 37:
John Horton, age 7 male, white, born England, mother and father of foreign birth, attended school
Walter Horton, age 4, male, white, born New York.

Then in the 21 June 1880 census, 3rd Ward Hudson, page 22, ED 18 at 172 Union Street:
William Horton, white, male, age 45, married, sexton, born England as were his parents.
Catherine, white, female, age 52, wife, married, keeping house born Ireland as were her parents.
John T., white, male, age 16, son, single, attended school, born England, parents born England.
Walter, white, male, age 14, son, single, born New York, parents born England.

So it seems after Eliza died two of their children John and Walter lived for a time at the Hudson Orphan Asylum then after William remarried they joined the family. I couldn't find William Jr. in the 1880 census at Hudson and there is no death notice in the above mentioned book.

Susan