It is tempting to spray glyphosate (click for sources) or an organic non-selective weed killer (click for sources) on green winter weeds when your lawn grass is brown and dormant.
However, bermudagrass is the only turfgrass on which I’d recommend this practice – – and with much caution.
The bermudagrass must be completely dormant. Get on your hands and knees to examine the base of the grass plant. If you see ANY greenery, DO NOT spray herbicide on the lawn.
Other winter-dormant grasses, such as centipedegrass, zoysiagrass and St. Augustinegrass NEVER go completely dormant. Therefore it is too dangerous to ever spray non-selective herbicide on them.
There IS a way to use a non-selective weed killer though.
Wrap an old cotton towel or T-shirt around the tines of a leaf rake or yard rake. Spray herbicide on the cloth until it is saturated. “Paint” the weed killer onto the green weeds that are growing above your dormant grass stems. This can be done to ANY of the winter-dormant lawn grasses.
The results will not be immediate but you’ll see damage to the weeds within a few weeks.