Ask Mr. Smarty Plants

For openers, 4" to 6" pots are a little small for a flowering plant. You are most likely going to want something bigger so enough soil to accommodate roots and hold moisture can be used. The second problem is that one hour of sun is not going to be adequate for many flowering plants. If you go to our section on Recommended Species, select North Central Texas, and Narrow Your Search with "herb" under Habit, and less than 2 hours a day under Light Requirements, you get three suggestions:

Aquilegia canadensis (red columbine) - upright, 1 to 2 ft. tall

Lobelia cardinalis (cardinalflower) - 1 to 6 ft. tall

Rudbeckia hirta (blackeyed Susan) - 1 to 2 ft. tall, biennial, flowers the second year

So, we went hunting for other plants native to Texas that might work in such a space, but not necessarily flowering. We found these ferns that would hang gracefully over the edge of a hanging pot, but would definitely need more than a 6" diameter pot to flourish:

Adiantum capillus-veneris (common maidenhair) - 6" to 1 ft. high

Onoclea sensibilis (sensitive fern) - few inches to more than 3 ft.

Phegopteris hexagonoptera (broad beechfern) - 1 to 2 ft. long

And, finally, a couple of dark horses:

Dichondra argentea (silver ponysfoot) - really a ground cover, and does better with more sun, but could do well in a hanging basket

Phlox stolonifera (creeping phlox) - a mat-forming perennial, 6 to 10" tall, semi-evergreen foliage and lavender, blue or white flowers

It would seem you need to rethink your plans for that area. There are some native vines that can get along with low sun, but they certainly will not remain confined to a small pot. Under eaves and north-facing are factors that combine to shade a plant from the sunshine necessary. 

Aquilegia canadensis

Lobelia cardinalis

Rudbeckia hirta

Adiantum capillus-veneris

Onoclea sensibilis

Phegopteris hexagonoptera

Dichondra argentea

Phlox stolonifera