There is very little likelyhood that a $40 sleeping bag will keep you warm when you are snow camping. On snow you will need a good insulating pad underneath you, a good quality sleeping bag, down if you can afford it and keep it dry, a good quality (wool is good) hat and good socks to stay warm. You should also keep something high in carbs to eat during the night to refuel your furnace when you get really cold.

You can't compensate for inadequate insulation between the snow and your bag, but if you have a marginal bag you can at least sleep in your clothes to make up somewhat for the bag.

Snow camping should not be taken lightly. Things can become very difficult and dangerous for you in a hurry if you are not properly prepared.