So last winter we came across this problem. The kids were out in the snow and their hands were getting wet through their gloves. It didn't matter if they were knit gloves or the kind that are supposed to be waterproof. They were getting wet. You can't tell a kid they can go out in the snow but not get their hands in it. You just can't.
I decided to remedy this problem in the only way I could at the time. There was no way to get new gloves that were quality and waterproof in the short time that we had snow. Plus the stores were out of gloves anyway. So I did the next best thing. I went to the grocery and bought kitchen rubber gloves. Yup I did!! I bought them in sizes that would fit over their gloves. I put their stocking gloves on their hands and then stuck a rubber glove on top. The gloves were long enough to go over their wrists and prevent snow from getting in there. Then we put their coats on and Voila! waterproof gloves. They went out and could touch the snow, play in it and get in all kinds of trouble out doors. The rubber gloves helped them grip on to their sleds and form a great snowball without the snow sticking to their gloves. How cool is that??? The best part is that their hands didn't get wet at all, and neither did their gloves underneath! So when they came back in and then decided to go back out they didn't have to wait for their gloves to dry. They already were!