PegMc I was in Pearland, so also Houston area!  I grew up in South Texas, though (McAllen area).  I loved Houston, but it sure is easier to grow plants here.
It sounds like you sort of live in the sweet spot for anemones though.  Winters are a little too cold here in north Indiana.  Some people grow them but you have to fuss with tunnels and hoop houses, etc if you want them to do well.