Advice: Don't try to melt snow in your cup unless your using a gas camping stove in alpine conditions. It's very expensive on fuel and you can, under some circumstances, melt the cup. Snow is a very good insulator, being something like 50% air when it's on the ground. If you have lit a fire, put the snow in a barrier net (mozzie head net to most people) and hang it up next to the fire. Close enough to melt the snow, not so close as to melt/burn the net itself. Put the cup underneath it to collect the snowmelt.

Important point to remember: DEHYDRATION leads to HYPOTHERMIA.
That is because your body needs water in order to maintain it's processes. Including those that generate body heat. You lose water as fast in freezing conditions as you do in hot weather.