Traveling from Boston to New York Tuesday night. Light snow forcasted.
(What speed would a bus drive? MPH.
What speed would a train ride? MPH)
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.
1" isn't a storm, but it could combine with other factors to cause problems on the highway.
The snow will not affect Amtrak's Boston-NYC corridor. 1 inch of snow is nothing to them.
As for the highway, 1" generally isn't a lot... but that depends on how it affects the roads. Is it a temperature range where road salt works effectively? Is it a busy time when the DoT is making max effort to keep the roads clear? I've been out on Sunday mornings after an inch of snow, and seen road crews do almost nothing. It's certainly possible to drive in an inch of untreated snow, but it's more work and it's slower going.
In ultra-congested areas like Boston or NYC: you are very dependent on the behavior of other people. If somebody else has a problem, they can create a traffic jam either because of looky-loo's or lane closures, or they can flat out close a highway with a serious accident. Now everybody's cramming onto the detour routes which simply don't have the capacity.
It gets bigger and worse if a semi is involved, and they tend to be the first to have problems in bad conditions, especially if wind is added. I've driven stretches of highway with literally 100 flipped over semi's in the median or ditch... and not one single automobile.
Add to that, ordinary urban traffic jams.
2.5 cm of snow where I live wouldn't do a thing to bus schedules, unless we got rain prior - i.e. rain started freezing, and turned to snow. If that happens, all bets are off.
Also, buses tend to be pretty secure in slippery conditions. The vehicles are big and heavy, and have significant weight over their drive wheels. (This, from a local bus company that I asked on a very slippery day a winter or two ago.)