Yes, you can sod in Winter!
Winter sod is installed while dormant. Dormancy is due to low outside temperature and less water use during winter months. Winter dormancy in turf is the plants way of hibernating to protect itself through the harsh winter. During dormancy the sod will be a tannish brown color until temperatures and moisture increase in spring.
As long as your grade is set you can install new sod in winter even if ground is frozen. Apply starter fertilizer prior to installation, roll the sod out, pull seams tight and water using Turf Master Winter Water Guide (https://www.turfmastersod.com/water-requirements). If new lawn freezes after watering do not be alarmed freezing will not harm dormant grass. Once it gets warmer out the sod and soil will soak up the frozen water. On warmer days it is important to water the new grass. Utilizing a hose is preferred over a sprinkler system as it is easier to drain a hose and put it away until needed again versus an in ground sprinkler system. If you are using your in-ground sprinklers make sure to drain the back flow device or wrap it with heat tape to prevent any breaks.
Turf Master has been installing sod in winter for over 45 years with no issues. We have great success with winter sodding due to less stress on the grass during dormancy. Advantages of installing turf in winter are water savings, no mud and getting a jump on establishing your lawn for the upcoming spring and summer!
So, stop dragging mud around, cover up that dirt and get a jump on establishing a new lawn.