I don't know that I would choose it over something without a lot of white in it in a cold climate, but in Louisiana you'll be fine. In my experience, seasonal fashion rules have a lot less prevalence in areas that don't have winter.
Cute dress! Many of the fashion designers showed winter whites / creams for this season. And regardless, that rule is pretty out of date. The material / cut matters more than the color, and your example here is really cute!
If it were a linen shift dress, may be less "winter" relevant. But a pattern on white? Looks good.
The dress seems kind of summery to me, but it is hard to make a call without knowing what the fabric is like. That said, I'd think it would be okay in LA because it is still warm there.