When we say "herb," we mean herbaceous blooming plants, native to North America. If, when you say "herbs," you mean plants like rosemary, lavender and such, those are all native to the Meditteranean area and won't be in our Native Plant Database. Some of those non-native plants do quite well in East Texas, including Trinity County, but we won't be recommending them.
The second problem with your request is the "deer-resistant" stipulation. We have a list of deer-resistant plants; please read this disclaimer paragraph from the top of the list:
Few plants are completely deer resistant. Several factors influence deer browsing including the density of the deer population, environmental conditions such as drought, and plant palatability. Deer tend to avoid plants with aromatic foliage, tough leathery and/or hairy or prickly leaves or plants with milky latex or sap. Try using some of the plants listed here to minimize deer damage to your landscape."
Further complicating this problem is the fact that there are only 346 plants on that list, and that constitutes the deer-resistant plants for North America, including Canada but not including Mexico. By the time we sort that list down to not only Texas, but East Texas, there will be very few choices. First, we will go to our list of Deer Resistant Species and then, using the Sidebar on the right-hand side of that page, we will select on Texas for the state, and nothing else, so that we will get a list of all plants in Texas having exhibited some deer resistance. Caution: You will need to read the whole webpage on each plant; some of the indicators will be "Highly Resistant" under deer resistance, some will only be "Moderately Resistant." Our examples are all Highly Resistant.
For each plant on our list, we will go down the webpage to the bottom and click on the link on that plant to the USDA Plant Profiles. This will get a map of all of North America, with the states where that plant grows in green. Since we have stipulated Texas for the state, it will always be green for the plants we have listed. Click on the state of Texas, and you will get a map with the counties where the plants grow in green. This is a good one to check on each plant, because there are so many different ecosystems in Texas, and some of the other areas in Texas might be distinctly hostile to the plants for East Texas, in terms of heat, soil and amount of rain.
Before we present you with our list, we are going to add some plants you did not ask for but that deer do not generally care to eat. There are a number of native grasses and grass-like plants that are very attractive, hold their places all year, some needing sun and some part shade. These are not lawn grasses, and you will need to check each webpage to see what they require.
So, here is a list of the plants on the Deer Resistant list, native to Texas. We will also check that each one we list is native in or near Trinity County, Texas.