Unfortunately the only information I came up with was that the records of 2nd Orange County Militia were destroyed in a fire in Albany in 1911. I was able to locate Cornelius Cor Smith's homestead and mill (1760)in Tallman, NY. The home is still there but the mill was gone. Just foundations left for the mill. I used old maps to locate it.
As far as specifics on the participation in battles of the Regiment, I have not had any luck. I have not done any research lately but will resume in the spring. If I locate anything that may help you I will let you know. Good luck!
PS: Thank you for the information on "Winter Soldiers". I will look it up.