Other fabrics may be worn between the two periods. Would these periods depend on temperatures rather than dates like the old white between Memorial day and Labor day rule?
Another person in Texas, Austin to be specific, although I lived briefly in Dallas and twelve years in Houston. For the past decade plus, the patterns for winter and spring have been quite variable. Tweed had a good run this year, but linen felt right many days, too. I pick fabrics by temperature. I still leave the seersucker home until Labor Day. For linen and Madras I am more flexible. I often find a tweed jacket and tropical worsted pants a good combination. Flannel days are rare.Tweets from January 4 to January 6. Linen from February 1 to December 15. Just kidding although I do live in Texas. Truth is I only own one tweed sport coat now and rarely wear it. Summers are often pretty hot so unless I will be in air conditioning the majority of the day, jacket comes off until I get back inside. I have never liked driving wearing a sport coat or jacket so always remove and hang when getting in the car.
I think in the post covid world you can pretty much dispense with the old rules in almost all circumstances.