There can be a lot of variance between the official records on snowfall amounts, and personal experiences regarding how much snow has fallen in certain periods of time. Part of this is because data collection methods have changed over the years, and also the fact that snowfall amounts aren't collected in all areas, all of the time.
Further making it difficult to isolate the greatest snowfalls is the fact that many places have not been keeping records for all that long.
The most meaningful way to discuss snowfall amounts, then, is to rely more heavily on personal experience, at one location. Even then, there will be discrepancies between official documentation and what people experienced.
A case in point is a National Park I'm very well acquainted with. Officially, the average snowfall there is 184 inches a year, or just a little over 15 feet (about 5 meters). The problem with these numbers is that they only come from one relatively sheltered location, and they aren't too accurate.
I recall numerous years in my youth, when a snowstorm would drop roughly a foot of snow an hour. It is pretty easy to see that just a couple of those storms would drop well over 15 feet of snow. In fact, it was not uncommon to have 20-foot snow banks for several months.
Yet, I recall a ranger once saying on a news station that the park had received 6 feet of snow in 8 hours. This was something she referred to as "a record amount of snow to fall in only 8 hours". My initial thought was that she needed to look a little further back in the records, until it occurred to me that the way the records were taken and maintained, from her perspective, it was undoubtedly true. She had not lived there long enough to know different, so she was basing her statement just on what had been written down.
The greatest snowfall in the history of the park, that I personally recall, happened in the spring of 1968. There had been several weeks of warm weather, and the snow had begun to melt. As was the habit in that park, road and trails crew took the opportunity to remove snow from the parking lot in front of the building known as the 'cafeteria'. This location is about 7,000 thousand feet, and the snow clearing is part of the park's yearly opening.
Crews were working away, when they saw a storm coming in from the south. Figuring that it would be no more than a squall, they left their equipment where it was, including a Cat D-9 which was left running, and they headed down to headquarters to wait the storm out.
The storm hit about an hour later with enormous fury. Since the air was warm and moist, the first snowflakes were wet and large. These were backed by fierce winds. Within eight hours, some houses were sealed shut because of blowing snow that partly melted, then froze again. At the end of the first day, temperatures had dropped, but the snow continued to fall in the form of very small flakes or powder snow. Snow accumulations at that point were at about 12 feet and growing. There was a nearly continuous white out, and even plow crews were sent out only sparingly.
Three days later, the storm finally blew itself out. Over 25 feet of snow had fallen in that brief period, and wind drifts totally covered many of the two story houses. The extent of it wasn't really known, though, for another three weeks, when the weather conditions were again such that the crews could finally return to clearing the snow in the parking lot by the Cafeteria. They found that the Cat they'd left behind was buried under a 100-foot snowdrift, caused by high winds driving the snow around the Cafeteria.
Needless to say, the opening of the park was delayed that year.
More staggering to my mind, a storm that had occurred in 1942, before my birth, apparently dwarfed that 1968 storm.
It is very hard to get the true measure of the greatest snowfalls in history, even when you've been through some very heavy snowfalls. The numbers recorded on some document or electronically somewhere just don't do justice to the amount of snow that has fallen. One thing that we can say with some certainty though, is that few people want to go through the experience of such a large snowfall.