Ordinary aluminum foil will work, but it is flimsy and will blow away easily. Heavy duty aluminum foil will work, but two layers of it mashed together works as well. There used to be an Extra Heavy Duty aluminum foil sold locally, but it is almost impossible to find except online and only in industrial quantities. The heavy duty stuff is also good since many of the rolls of it are extra wide. When you are trying to make a big enough cap to cover the entire snow melt pot, that extra width is handy. As a flare shield against the tent, the extra size is critical.
You can always melt snow outside of the tent vestibule, but that is a pain when the weather is bad. That's why you collect clean snow into a clean garbage bag when you first set up the tent. Then you wedge the bag into the space next to the vestibule, perhaps between the inner and outer tent. If you do it right, you sit inside the tent, and you are reaching out into the vestibule where the stove is burning. You can scoop more snow into the pot without getting in the weather.
For snow melting with a typical backpacker stove, I recommend you to have a piece of thin Masonite board, maybe one square foot, to act as a stable base. Otherwise, the stove will slowly melt its way down into the snow. I was practicing this just last weekend.