Here in TX, there is NO bag limit, NO closed season BUT we usually (due to worry about contracting "rabbit fever") hunt them, in northeast TX, only after the first hard frost of the year.
Fwiw, my 1st cousin, some years ago, took 22 cottontails & "swampies" in ONE afternoon with his .40 caliber TN Pore Boy.
(Like I said, both varieties of rabbits are REALLY numerous here. = My sister one fall evening counted over 40 between the front gate & our farmhouse.)
yours, satx