Keeping on and off the grass
There is a chance in a mild December that a last mowing is needed, and while it’s good to wait until March/April time to mow a new lawn sown from seed in autumn, it can be done now on dry, sunny days.
Set the mower or cutting deck on a garden tractor to a high setting. Cutting the grass too short will encourage moss. Brush off earthworm casts which can encourage weeds and moss as well.
You might be planning to grow a lawn from seed in the spring so digging the area now will let the frost and winter weather break the soil down to a good, workable tilth.
Keep an eye on any areas where water may sit on the surface. These will need spiking and aerating in the spring. Keep off the grass when it’s frosty, it just damages the grass if you walk all over it.