Although native grasses sometimes will remain green into late fall, they really have not made any substantial growth since early September. Rather, they are storing energy and nutrients for winter. The most important thing you can do during fall then, is to allow the stand to rest so nutrients and energy still in the above ground portions of the plant can translocate back into the roots. Like all perennial grasses, those reserves are critical, providing energy required for respiration during dormancy and for rapid growth when favorable conditions return the following spring.
If you have much remaining material on the pasture from the previous year’s growth, you have basically three choices: clip with a rotary mower, graze (likely with some level of a protein supplement), or burn in late March. Clipping really is not necessary, unless for some reason you have an unusual amount of material left standing. In that case, you may want to evaluate your grazing management during summer and adjust so that at dormancy, there is a more appropriate amount of residue, maybe 18-24 inches.
Grazing will provide support for animals, but not any gain. In the Great Plains, folks commonly will graze such material and use it for a portion of their winter forage. A study here at UT grazed heifers on this material for 100 days (Jan – early April) with a protein supplement and found that each animal could be supported by about 1.5 acres. Regardless of the forage value, it is a way to remove unwanted material.
Burning, which is a good practice for native grasses, should be conducted at the end of winter when plants are beginning to break dormancy. Burning earlier in the winter can encourage cool-season weeds. On the other hand, a burn in late March-early April will allow the natives to begin growth about two weeks earlier (blackened soil is warmer) than normal, reduce weed competition, and improve forage quality.
Fertilizer should not be applied on natives at the same time as it is on cool-season grasses because of the different growth periods of the two grasses. With cool-season grasses, some amendments are commonly applied in the fall. Doing this to a semi-dormant warm-season pasture or hayfield will be a very poor investment – the grasses will not be able to use the nutrients, but weeds will! The same applies in spring – wait to fertilize in mid to late April when the warm-season grasses are growing rapidly and can take advantage of the increased fertility.
As is the case with cool-season grasses, fall (for thistles and other biennials in their first growing season) and late winter (buttercup, plantain) can be good opportunities for weed control. The timing is the same for warm- and cool-season grasses in these cases. On the other hand, a big difference with dormant warm-season grasses is that you can also use broad-spectrum herbicides (i.e., glyphosate) to suppress cool-season weeds without injury to the warm-season grasses. If you are a bit late in use of broad-spectrum herbicides in the spring, the plants will be forgiving (especially switchgrass and eastern gamagrass; bluestems and inidiangrass, a little less so). But in the fall, plants that are still green, even after a frost, can be vulnerable to injury. So if you are going to use this approach, wait until February or March.