One inch (2.5 cm) of falling snow changes pretty much nothing. Even more so for a heavy vehicle.

Snow melts easily by the passing of vehicles and so most motorways do not have more than a very thin layer of snow after an inch (2.5 cm) of snowfall. At 4 inches (1 dm), it starts making a difference, depending on the rate of falling.

Both bus and train take between 4 and 5 hours, only the bus is more affected by traffic, so if you arrive around rush hour (which is pretty long in NY), the bus might take even an hour longer than predicted.