I go kayak fishing on Christmas & Drum Bay often (which is 5 mins from Freeport).
During the duck season, I've seen duck hunters line up the shorelines that face north in the mornings.
There's other spots around and have seen hunters use kayaks to get to them.
Which makes sense, since the water depth can be as shallow as 6" during winter low tides. You'll get stuck on a boat.
Much of the marsh area are legal public hunting grounds.
But like RiverRunner says, check with TPWD to be sure.
God Bless Texas
Remington 1917 - 30-06
Stoeger P350 - 12 Gauge
Diamond Edge SB-1 - Compound Bow