Since the poster mentioned Metro-North (not Amtrak) are we talking about suburban trains on the Harlem and Hudson Divisions? From 1996 up until the past year I think Metro-North if anything, did better
than Central used to do. And I am very very sorry to have to say that.
This is based on my experiences over about fifty years of regular riding, too.
We had a 20 inch blizzard back in 2004.That afternoon, as soon as the snow stopped I went to the Tarrytown station to see if the trains were running. I found that not only were they running, the express from Poughkeepsie arrived only ten minutes late. I remember telling the conductor, when he came around to collect my ticket, that I found it amazing they could come down from Poughkeepie just as the blizzard ended and be only ten minutes late. He proudly said, "We try!"
Another factor though, without getting into a thing about climate change, snowfalls over 10 inches or so were relatively rare in the 1950s and 1960s. Yet anyone who rode back then knows, when it happened you were in for trouble.
Did they shut down completely? First time I remember that was in February 1969, but that was already Penn Central.
What I remember is, Central suburban trains would be late, chaotically late but they would run. The 'morning after' was when you might have train service shutdown for a while. I wasn't around for the 1947 blizzard but I think Central did shut everything down for a while. But not 48 hours (as happened last weekend during Tropical Storm Irene), not even close. Of course back then it was TOUGH to get accurate information. Call the local station agent and HOPE he answered and, if you got through, HOPE what he told you was the real deal. Sometimes they'd just snap, "Yeah they're running," and hang up.
I have read old news articles about the famous Blizzard of 1888. That one shut the Harlem and Hudson down but for about 24 hours only I do believe.