I am in South Carolina. I do not weed, at least for the past 5 years. I depend on the properly maintained grass to control any weeds. The winter rye grass seed I order from my local feed store. I have used a number of types, buying what is designed for winter horse and cattle forage in my area. I am currently using Attain, a hybrid which was developed at the University of Florida.
I have found over the years that what I save by not having to buy much hay in the winter essentially is about what I spend on the winter rye grass seed plus fertilizer for it. But the horses get to forage and graze on green grass all year versus baled hay. And I have far fewer hay bales to lift.
In fact I use so little hay that I now just pick up Standlee compressed bales at Tractor Supply a few at a time as I need them. Which cuts out the worry about finding good local hay and storing it.