The Lubbock, Texas mission experiences all 4 seasons. The winters don't get a ton of snow, but it is really cold. The summers are hot. The temps can range from about 0 degrees to 110 degrees, so packing should allow for all the climates. It is not crazy rainy, but when it rains, it really pours. They have sudden bursts of thunderstorms that really drench you. It is pretty common for the streets to flood.
During the winter, you will be grateful for layers and especially thermals.
Blundstone boots are awesome to have (Sisters and Elders), especially in the cold- they are comfortable and warm. But, you can also find cowboy boots or something there that will work too.
Spanish speaking missionaries usually have a car because they need to cover large areas, but even then you'll do a fair amount of walking. There are some areas that are only biking and walking, though. Most of the mission is serving in small towns and cities. In the outlying areas of Odessa and Midland most people work in the oil field and drive trucks.
Everything you could need is available at the stores or can be shipped through Amazon.
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Serve shirts have a ventilation panel in the side of the shirt making them noticeably more breathable. Missionaries serving in hot or humid places absolutely RAVE about this feature. The most popular shirt for hot-climate missions, for sure.