This line ran from the border at Beechers Falls VT to Lime Ridge Quebec, abandoned in 1925. It went from QC into a remote part of Pittsburg NH for .75mi and then back into QC. Does anyone know if there is any visible evidence remaining in Pittsburg? RIght of way or abutments etc. Google maps doesn't show anything obvious, but it probably has been logged a dozen times since abandonment.
There is a short section of the Hereford that can be found on old USGS topo maps of Indian Stream and on the current Google Earth image of the area. You have to do some hunting. Go first to the old maps. You'll find the section of the railroad located along Halls Stream (on the border), north-northwest of Pittsburg village and probably a mile or two due north of Comstock Hill.
Then go to the Google Earth image of Cookshire, Quebec and trace your way south-southeast. It's easy to find the old roadbed from Cookshire to Sawyerville; south of there you have to look really closely. You'll lose it at times, but you'll pick it up along tree lines, gentle arcs, and highways down through some of the little border villages and into East Hereford. Some sections of it, I think, have been paved and are now used for local roads.
It appears that there was only a very short section, almost right on the border, that wound through Pittsburg. It looks like it might be walkable, though I wouldn't want to try it --- your presence would likely be noted by the Border Patrol rather quickly.