Ask Mr. Smarty Plants

When you say your house faces East, that doesn't give us a clear idea of how much sun or shade you have there. If there are larger trees in front of the house, you may have less than full sun, which we regard as 6 or more hours of sun a day. Part shade is 2 to 6 hours, and shade is less than 2 hours. Since the Phoenix roebelenii, Pygmy Date Palm, will grow from sun to shade, we will try to choose plants that are the same. The Pygmy Date Palm is hardy from USDA Hardiness Zones 9a to 11, and is native to Southeast Asia. At the Lady Bird Johnson Wildflower Center we are dedicated to the use, protection and propagation of plants native not only to North America but to the area in which they are being grown. The ones that fit that description are probably not as exotic and unique as you would like, but they belong here, which is environmentally important. 

Even though Spring is in Zone 9a, you apparently had harsh enough temperatures to do the plant in. We cannot promise we can find a native plant that is as exotic and as much of an accent as the plants that you lost, but we will try to find some plants that will be attractive and do well in the same spot. We will check to make sure that all our choices are native in or near Harris County, so we can know they are adaptable to the climate, soils and rainfall. Follow each plant link to our page on that plant in our Native Plant Database for more information on height, growing conditions and so forth.

Shrubs for Accent Plants in Spring TX:

Yucca treculeana (Don Quixote's lace) -has prickly points, like the Pygmy Palms, and may grow out of the size you have available for it.

Erythrina herbacea (redcardinal) - fairly exotic-looking, but the bright red seeds are toxic; probably shouldn't plant it if there are children or pets that might try to snack on them.

Sabal minor (dwarf palmetto) - fairly similar to the palm you lost. 

Leucophyllum frutescens (Texas barometer bush) - can bloom 12 months a year, depending on the rain, is evergreen, and the pinkish-purple  blooms are stunning against the blue-green foliage.

Ilex opaca (American holly) - this gets pretty big, but is a built-in Christmas decoration.

From the Native Plant Image Gallery:

Yucca treculeana

Erythrina herbacea

Sabal minor

Leucophyllum frutescens

Ilex opaca