The Red was navigable from Vicksburg to Shreveport though in the Red River campaign Porter's fleet got stranded at Alexandria and some
serious engineering was needed to refloat it. I gather from the various sources I've looked at that the low water was a seasonal and also intermittent thing (in this case,
late April and early May).
Atchafalaya ("White" Lake & Western Branch on the map):
The Union forces wanted to open up the Red River which was an important source of supply for the Confederacy. On April 20, 1863, Opelousas and Washington fell to the Union forces. Earlier during the year there had been a Federal operation with gunboats on the Atchafalaya River. Several times during that year, Port Barre area was center of skirmishes. One was the attack of the Federal steamer, LaBelle, at Barré's Landing. There also was a heavy skirmish along Bayou Courtableau on May 22, 1863 , which was the result of the Union Army hauling off a boatload of captured bales of cotton from Washington. Further down Bayou Teche, Butte La Rose had been captured by the Union Forces and Opelousas fell to General Banks on April 22, 1863.
Both were navigable, though from other sources I gather not in winter (
here the reference is to November) and in periods of low water - winter and the dry season, with intermittent interruptions as well.
Vicksburg guarding the back door:
The Confederate leaders also recognized the strategic importance of the "Hill City" of Vicksburg, where the railhead provided a two-way supply route into Arkansas, Texas, and Louisiana to the eastern Confederacy. Supplies from the Gulf of Mexico ports could also move up and down the Atchafalaya and Red Rivers.
[Edit]
Boating season on the Red River...
Navigation on the Arkansas and Red rivers was difficult and dangerous due to snags and frequent low water. Boats often attempted to go upstream almost year round, but the usual "boating season" ran from January to June. Although seasonal, high freight rates made steamboat operations on these streams economically attractive.
Seems the same applied on the Atchafalaya, with some boat captains getting mules to haul their boats through the mud rather than wait for the next high water.
I think from all this (and more) that the Atchafalaya should start freezing in the autumn (October) and start to unfreeze in very early spring (January, when the Mississippi starts to rise) to simulate the effects of winter and - to some extent - low water periods.