The main problem with the train will be parking. Since, you're on the Ossining side of the county, take the Hudson Line train to Grand Central Station. I would strongly recommend going to the Croton-Harmon train station as the village does have a specific section for overnight-long term parking. You must check-in with an attendant in the building on Gateway Plaza that's grey with a blue awning. And, you must pay in person, in advance. They are open until 8pm weekdays, 6pm Saturday, and 4pm Sunday, but I believe this is only for payment and you can retrieve your car at any time.
Here are a couple of links for you:
Mta-MetroNorth Hudson Line Schedule/Fares:
mta.info | Metro-North Railroad
Parking at Croton-Harmon overnight/weekend:
Village of Croton-on-Hudson, NY - Overnight and Long Term Parking