Can I carry snow with me, in order to melt & boil at another location?

Snow isn't carried as part of your inventory, it's simply abstracted as the ability to make water at literally any fire.

The closest thing to this - and it's of limited usefulness - is, basically, parboiling water: You can melt it to non-potable water, which can then be boiled to be safe to drink later on; you can also then purify it with purification tablets. The only real use for this is if you've already got a fire going, but feel the need to relocate and you're allergic to wasting firewood (like I am). You can use up the committed fire energy making non-potable water, and then finish the job elsewhere.

Water Purification Tablets let you double your water production per unit of time and/or firewood in this way since melting the snow takes the same amount of time as boiling the non-potable into potable.