Leveling Zoysia in Winter

Q: Can you level a zoysia lawn in the winter when it is dormant, then fertilize in the early summer or is it better to do it all in the summer? This is my first zoysia lawn and I thought it would not be as thick when dormant and the sand and soil would fill in better. Is that correct?

A: My prediction is that it will be damaged by the wet sand/soil on the plant crown during winter. Do the leveling in early summer for best results.