Ask Mr. Smarty Plants

First of all, we are sure you know how very frequent burn bans have been and are going to be in our continuing drought and heat in Central Texas. And, frankly, it would serve no useful purpose. Wood ash is very alkaline and guess what our soils are - alkaline.

Just to reinforce my point, please read this article from Gardens Alive, answering the very same question. And, near the end of that article, note this comment:

"Oh, and if you live in a naturally alkaline area, like some of our Oklahoma and Texas listeners, you shouldn’t add any ash to your lawn or garden. Instead, try using large amounts to kill problem weeds like kudzu and thistle by raising their soil’s pH to plant-deadly levels—horticultural vinegar in reverse!"

We had never heard of that solution before, and don't know that we would recommend it. But we do feel in all our wind, a great deal of that alkaline ash would promptly blow somewere you did NOT want it. And even if you did use that treatment to kill some noxious weeds, you would then be left with soil that was damaged for a long time to come and would probably have difficulty getting anything more attractive or useful to grow there, including our own native wildflowers.

Perhaps you could reconsider shredding. There seem to be many companies around that have that service. The freshly shredded wood chips would not be suitable for use as mulch or a soil additive until they had been thoroughly composted, but for paths and areas you wanted to shade to avoid weeds coming up, they would work very well.