I guess it depends where in Texas, but overall I do believe that Texas is quite a bit warmer than Missouri! Check with SMRobs -- she can give you the outlook there!
Blanket? Yes, in theory the warmer she is, the easier it will be to put weight on, but I think she has more going on than needing weight. I don't like the look of her belly. You can blanket and feed all you want, but if she isn't digesting properly it won't help anyway. Have you checked for worms?
I took in two thin horses late in the year and didn't blanket either of them. I did make sure they had a good shelter (actually a free-run barn) and access to three sides of the barn also so they could be in the sun and out of the wind. I fed them like crazy -- hay, hay and more hay. They got a bit of supplements, but it was the hay that kept them warm. They never showed signs of being cold. If they were, I guess they went in the barn together.
Your mare looks like she fits in well with the herd and that will help her also.
So, blanket or not? I vote not, unless you see signs of her being cold, or she starts to loose weight. She may not gain much over the winter though. My reasoning is that 1. The blanket restricts the movement of the hair follicles that adjust as needed according to the temperature at any given time, 2. It's another thing that horses can get tangled up in, 3. She may still develop a thicker coat if you don't blanket her, but she likely won't if you do and 4. If there is a time in Texas that it's actually cold, if she really hasn't developed enough of a coat by then, you can still throw the blanket on her for a couple of weeks just for the "cold snap"...
I'm just giggling here about "cold" in Texas. Here's from Wikipedia: The worst cold snap to occur statewide occurred during the last half of December in 1983. Four stations recorded their longest continuous readings at or below 32 °F (0 °C) on record. At Austin, Texas, the temperature remained at or below freezing for 139 hours. At Abilene, Texas, the period at or below freezing totaled 202 hours. Lubbock, Texas saw temperatures at or below freezing for 207 hours. The Dallas-Fort Worth airport measured temperatures at or below freezing for a total of 296 consecutive hours. Snow which fell on December 14 and December 15 across northern Texas stayed on the ground until New Year's Day of 1984.
Now I have to look up Missouri -- this should be good...