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The reason it seems weird to you is that it's flat wrong. It takes no metabolic water at all to melt snow after you eat it, so there's a net fluid gain, not loss. What it does take is a fair amount of heat. When you burn fat to produce heat, one of the products is a small amount of water. Consuming very cold water will therefore result in a tiny additional fluid gain versus the same amount of water warm. Thus, if they say it takes "too much energy" to eat snow, they may well be right. If they go on to claim that somehow results in a net fluid loss, then they're not right. There is a phenomenon called "cold diuresis" that increases fluid loss when you're cold, but this is likely to be a factor whether you're eating snow or not.
Look at it this way: there's practically no difference in energy transfer if you eat 500 grams of snow at 0C compared to drinking that half-liter bottle of not-quite-frozen water you found in your trunk at 0.1 C. Either one will result in exactly the same fluid gain and either will chill you almost exactly the same.
You're probably better off melting the snow if you can, but you're also better off warming the water if you can do that, too. If you're reduced to munching snow to quench your thirst, you probably don't have a lot of heat or energy to spare. One way to look at the question is whether you'll die faster from dehydration or hypothermia. Almost always, the hypothermia will get you much faster. If hypothermia isn't an issue (for example, you have tons of chocolate for calories and masses of toasty goose down insulation), then dehydration is one of the most likely causes of death in the wilderness, so in that case eat as much snow as you can get!
The main reason not to eat snow is that it's totally filthy since the nucleus around which snowflakes form is some tiny particle, usually of soot or bacteria.
I really doubt chickens would be able to consume enough snow one little beakful at a time to lower their core body temperatures significantly.