Hello, I don't think it is a matter so much of what to apply, as much as what kind of grass is planted in your lawn and what kind of weather you have in winter. Some lawns are planted with winter dormant grass. They will not green in winter unless you over seed them with another variety. It would be helpful to know where you are located and what type of lawn you have.
it depends on the soil some soil has alot of clay in it which is not good cos the roots cant grow down into the soil what I suggest you do is add lawn food cos the grass needs plenty of calcium and magnesium, the frost and cold causes the photosynthesis to change but thats normal so just let it go and see what happens.