Depending on where you live, the ground temperature under the basement floor is the same all year. That is about 55 to 63 degrees. With a normal room temperature of 70 degrees, you don't need much insulation to keep the floor isolated from the "cold" and it doesn't get worse with the winter season.
I think the carpet pad with a rug will be just fine as long as you don't have any moisture problems. Check your floor for moisture penetration by tapeing a 2x2 foot square of plastic to the floor for a couple of days. If you remove the plastic, and the floor appears dry, then you should have no problem with putting a carpet directly on the floor. There is no sealer that will keep the moisture from penetrating.
One other note, if you have forced air heating, make sure you have a cold air return at the floor level to keep the cool air from "pooling" near the floor.
Good Luck!
Dodgeman