Normally, this suits me just fine (outside populated / popular recreation areas, of course -- I'm not fond of drinking dog poo or skiing wax). As long as I am moving about I usually have plenty of surplus heat which needs to be removed, one way or the other. Using a few calories of surplus body heat to add a bit of water in my tummy seems like a brilliant idea to me. But a mouthfull of snow doesn't have many grams of water, so this practice is just a fraction of my water consumption. And I stop eating snow when activity stops or if I start feeling cold.

On my last trip I re-learned old army tricks from my army officer friend:

• A water bottle has a wide mouth, making refilling with snow easier
  
• You start re-filling with snow immediately after your first sip, always stuffing it full (so it always contains water with snow in it, which will melt quicly, not "wet snow", which melts slowly)
  
• in sub-freezing temperatures you wear the water bottle on your body, under your outer layer of clothing

Now the water-bottle-on-your-body trick isn't really nescessary for your average day hike unless it is REALLY cold. A water bottle doesn't freeze for many, many hours if it's inside your backpack, among your extra clothes and whatnot. But the practice is sound, and something I'm happy to adapt for trips to remote areas.