I would guess that you just want it to stay succulent
to hold down the carbon-nitrogen ratio in the mowed
plant residue, unless you are mixing it with a legume
(like hairy vetch or clover or field peas) to supply extra
nitrogen and want the rye to provide a structural support
for the legume (in which case you might hold off
mowing it until it flowers):
This page says cut it at "12-18 inches":
http://www.uvm.edu/vtvegandberry/fac...winterrye.html
In your Gulf Coast climate, it probably is not critical
whether you mow it now or not. If you do, odds are
it still grows plenty over the winter, just like it does
in spring and summer for people in climates farther
north who mow it before it flowers. (Winter Rye
has been kept alive for 7 years by letting it grow
and then consistently mowing it before it flowers.)
You need to let it flower in spring if you want mowing
to kill it. Shallow-tilling mowed winter rye that has not
flowered will not work, it will keep coming back. Then
one ends up needing more drastic measures, like covering
it with black plastic for weeks or using a herbicide like
Scythe (pelargonic acid) to kill it that only works on foliage
and won't have any herbicidal effect in soil (thus not
affecting subsequent seeded or transplanted crops
there).
Winter Rye flowers when the day length gets to 14 hours,
so you can watch the sunrise-sunset difference in your
weather report to know when to give it the "fatal last
mowing". (This could be a big hassle around the equator,
where the days never get that long.) You might get
a few late-flowering individual clumps that survive
because they haven't actually flowered yet that
need to be forked out of there.