Just bring it with you. You can’t check but there is a lot of room on overhead racks. The Amtrak from Boston to NYC is great especially if you take the Acela, which is a nicer, faster and doesn’t make as many local stops. Try to sit on the left hand side facing front of train if you can for best views of the New England coastline on your way down to NYC.

Just show up 15-30 mins early as others have said. If you leave from South Station you have to wait in the big departure hall until they assign a track and say you can board.

Don’t fuck around with winter hikes in the Whites unless you REALLY know what you’re doing. People die doing that on a regular basis.