Middletown Springs is in Rutland County, Vermont, the name was changed from Middletown.

Windsor County does not have a Middletown.
However, Vermont Place Names, by Esther Munroe Swift, states that the Town of Andover in Windsor County had an area called Middletown.

1800 census for Andover, Windsor Co, VT has a Jacob White
1790 census for Middletown Springs, Rutland Co, VT has Abraham, Caleb, and Nicholas; a Gregory, Nehemiah and Philip are in Tinmouth, also in Rutland County.
1800 census Wallingford, Rutland County has Abraham, Coolige, Elijah, Nehemiah, Nicholas, Philip, and Simeon White

I have no connection to this family. Good luck with your research.