The only census which seems to include the Nathaniel and Ursula (Wright) Searing family is the 1810 for Saratoga Springs:
The census includes Nathaniel Searing and the members of his household. Unfortunately, it wasn't until 1850 that all the household members are listed in the census. So, we can read the number of people of each age. This would count for Nathaniel, Ursula and their three children plus 4 other people. Yet, we can't tell for sure who is included.
If Nathaniel Jr's obituary is correct, Nathaniel Sr died about 1826 and Ursula about 1830. I do not find the family in the 1820 census. Maybe by then they were living with relatives, such as Samuel Searing, father of Nathaniel or Richard Searing, brother of Nathaniel Sr.
Exciting Searing Happenings
6 months ago