Not sure where you are located, but here in NC it gets cold in the winter with some warm days still mixed in. Just because it's cold doesn't mean the roots aren't doing anything. Now it the ground is frozen solid that's another thing. If it's bermuda it will just sit there until it warms up and start growing.
Is it new construction? If so it is a lot cheaper to lay the sod after the crew has been there installing plants and grading the area. They would need to have some type of erosion control regardless. So either rye, sod, or straw.