The narrative about this Cold River Road farm from the 1976 Clarendon History book can be found at the link above. That narrative terms it the Nelson Farm after the then resident living there, Blanche Balch Nelson (1892-1980) but it was the Parker Farm for the first several generations.
Current (2017) research expands upon the origins of the farm from what was in that 1976 article. Benjamin Parker (1758 - 1813), a Revolutionary War soldier from Groton, MA, came to Clarendon ca. 1780. The farm passed to his son Benjamin (1784 - 1868) and then to the two sisters noted in the 1976 article. They were Mary Abigail (1823 - 1895) and Sarah (1825 - 1896). Neither married. They stayed on the farm with their mother Patty Wyman Parker (1786 - 1877).
The transition to the Bidgood family can also be expanded upon from what was known in 1976. Jacob Bidgood grew up in Clinton, NY but his wife Rachel Parker Thomas (1837 - 1913) was part of the Parker family. She is found in that household as a 12 year old in the 1850 census and by the 1870 census she is there with her husband Jacob Bidgood and Patty, Abigail, and Sarah Parker. Rachel's mother may have been a Wyman and thus Rachel was possibly a niece or grandniece to Patty Wyman Parker.