Without reading other answers:
The process of melting it and keeping yourself warm actually uses more water than the snow will provide. You can dehydrate yourself and speed up hypothermia by eating snow. Make a fire to melt it to use for drinking.
Raised in Virginia, near Washington, DC
This is also a problem in many remote areas of the US, which does include areas between some major metropolitan areas. Silly Dutch tourists, you can’t just drive from NYC to LA for the weekend. It’s a several days journey with much of the western part of it going through hot, dry desert areas. Bring water. I’m so seriously.
Count me in the group that would not have known why one shouldn’t eat snow-- despite growing up in Minnesota.
But I lived in the suburbs of the Twin Cities (Minneapolis-St. Paul), and didn’t do much wilderness survival stuff.
[spoiler]It’ll rapidly drop your core temperature and you’ll be hypothermic before you know it.
Also, it might be yellow snow :)[/spoiler] What do you know, all that cold-weather stuff they taught us in (South African) Scouts actually stuck.
This sounds like something “everyone knows” but it doesn’t pass the smell test for me. Various guidelines recommend somewhere between 2 - 4 L of water per day. Given that you’re in a survival situation, let’s take the lower limit of this to start off with.
1 L of water is 1 kg and it takes 334 kJ to melt 1 kg of snow and then another 154 kJ to warm it to body temperature or ~500 kJ which is 120 calories. So eating snow is going to cost you about 240 calories which is about 10% more than your daily baseline, hardly anything that seems dangerous.
Put it another way, you see people all the time munch through a cup or two of ice that’s leftover at the bottom of their cups at restaurants. That’s really no different from trying to eat snow to remain hydrated but nobody is worried that people at fast food restaurants are suddenly going to keel over from hypothermia.
I’m going to put this one down as a silly myth unless someone can provide a reliable cite to the contrary.
People in fast food restaurants aren’t out in the cold wilds and have likely just, you know, eaten a calorie-heavy meal. The supposition here is that you’re in a survival situation. Very different situations.
I would think the only reason might be is that it will lower your core temperature.
Eating a cup of ice will lower your body temperature by a whopping 0.1C (0.2F). If that’s really the difference between you getting hypothermia or not, then the ice was not the problem.
Well, no. The point is not to exacerbate the actual problem (the “I am stranded in a snowstorm” problem)
Yes, but unless there’s evidence to show that it actually exacerbates the problem, I’m going to assume the entire rigamarole with a pot and melting snow is just an urban legend because the basic laws of science state that ingesting ice simply doesn’t have that big an effect on the human body.
I’d say any avoidable negative temp drop is going to exacerbate the problem. 2 degrees below normal is hypothermia. So this is a case where any drop is bad.
And cite for the 0.1 degree figure?
You also need to account for the energy to warm the snow up to the freezing point, although that usually won’t add too much.
I agree with you though that “never eat snow” shouldn’t be a dogmatic survival rule along the lines of “don’t drink salt water.” There’s plenty of cold-weather survival situations where hypothermia isn’t an issue and you’d be doing yourself more of a disservice by dehydrating yourself.
I’m going to guess this is a “your are already hovering on the brink of hypothermia” issue.
Canadian cross-country skiier here - I have drunk nearly-frozen water lots of times, without any concern about hypothermia - but then, I was usually very warm from exercise. I would not eat snow because it is not very thirst-quenching, it takes a lot of snow to make a small amount of water. But I would drink water from the springs at my dad’s cottage, which was very close to freezing.
On a side issue, we have a friend whose brother is married to a lady in Thailand, where he now lives; she has never been outside of Thailand and has expressed an interest in visiting Canada during the winter, in terms that indicates she has all sorts of romantic notions about winter and snow here, no doubt gleaned from movies - I don’t think it has been adequately explained to her just how very cold it gets here. 
I did this exercise, except it was about a plane crash in the desert. I remember the most important item was the lady’s cosmetic mirror and the least important item was the vodka. I guess it might save my life one day!
Yeah, I’ve slept outside in below-zero (Farenheit) weather, and I think “never” is way too strong a word. Particulaly when the OP threw in non-survival situations at the end.
It’s something to be aware of – 10% of energy can potentially make the difference in some cases – but hardly an absolute law.
One should also not leave the car during a blizzard/snowstorm if you get stuck. Far easier to find the car (and thus you) than to find the car and then look for you.
Spaniard, no fucking idea. In fact, we’d often… well, eat isn’t quite the right word, but let snow melt in out mouth rather than drink from our canteens, during hikes on snowed-on mountains (you don’t need to take your gloves off to grab a small handful of snow). During snowstorms we mostly did our best to not be there; huddling in the bus singing el señor conductor (“Mr Driver”, one of those songs you re-invent as you go) was definitely preferable to being out in the cold.
Here’s the thing, snow is mostly air, and it holds a lot of cold. There is very little water in a mouth full of snow. It’s like a drop. So the amount of cooling that you get far, far outweighs the benefit of the small amount of water that comes in.
And it cools you from the inside, which vastly accelerates hypothermia. By the time you are cooled enough to feel any symptoms you are too far gone to reach the conclusion that you should probably stop eating snow now. And you will still be incredibly thirsty and so you’ll continue to eat snow as long as you can manage to scoop it into your mouth.
Better to keep it in a bag in your pocket and drink it as it melts. When the baggie full of snow melts down to a half-sip of water this will all make more sense to you.
Hawaii/California. I learned to not eat snow and why from watching Man vs Wild.
Side note: What I lack in experience with snow I make up with in experience with Icees and Slurpees. Brain freeze hurts, yo.
From my experience, one doesn’t eat snow to quench one’s thirst, not because of hypotherma, but rather because it generally isn’t very thirst-quenching. As you note, it takes a lot of snow to make a little water.
In short, I do not think it is dangerous, so much as futile.