They generally stand well through the winter. Cut them back in the spring.

They are a warm season grass and those do best if divided in mid to late spring, just as they begin to push new growth. You can do it a bit earlier if you want and leave the foliage intact through winter, cutting back both the foliage and dividing the grass in March.

Attempting to divide in fall does not allow the root system time to re-establish before cold weather sets in and warm season grasses generally react poorly to that sort of root disturbance that late in the season.