Been a few years since we grew cotton, but we always shredded the stalks in the fall leaving them fairly tall to they will push over.  Then weather permitting refreshed the beds with hippers or buster/roller, and waited for spring. In the spring, burn down winter weeds and either plant into the stale seedbed or refreshed them depending on the condition of the row.

If your area still does any boll weevil eradication stuff they required you to shred the stalks to reduce winter habitat. Down here the stalks could live through the winter if you don't mow them.