Hey Austin! yeah, cool spell coming in Sunday night here. If it doesn't get below 34* the pepper plants will do okay. Protect from wind. They can be grown overwintered in home, but they need strong light, and watched for aphids as the winter progresses. Stuff doesn't grow too well in less than 11 hours of sunlight.
Serranos are small plants as all things go, they do fine in those pots. Jalapenos and poblanos, they are BIG plants, need much bigger pots. Use raised bed container soil if you purchase soil, but that limestone caprock you are sitting on won't bother them as long as they have room for the roots to spread out to hold them up. We sink the pots into the soil to shield the heat, but that is too shallow to do any good here. Strange summer as far as weather, so they didn't like growing if you put them out later than mid March. Peppers have different 'days to maturity' and that can affect the plants growth, after all, if you thought you would get peppers in 85 days, but it took 150 days, it could set you aback.
A favorite pepper site is Pepper Joe's pepperjoe.com
Different trees can affect plant growth as well, oaks secrete tannins that slow growth, other trees are allelopathic, such as elm and black walnuts and only select plants can survive under them. That said, Texas does require shade from 1 pm to maybe 5 pm in the summer.
My tabasco peppers started producing in mid Aug this year instead of lagging til Oct... I have always known August is the killing month here in the south for plants, because harvest starts in Sept... but this far south, nope, it is July that kills my plants. After the 3rd week in Aug the sun/heat breaks, the light starts shifting to the south more, and plants kick back in to trying to survive, so you get more fruits. I have a 5th round of tabasco peppers I need to strip tomorro before our cold spell. Always a Halloween cool down, but the last few years we have been fairly warm (almost 90*most of the time til Dec 1, ).
Let me see, this is the pot my tabasco does best in, but there is a bale of peat sitting up against the west side all summer, and a few boards to shield the soil across the sides. Tabasco get reasonably large, and I have grown a jalapeno in here, but I don't prune peppers, I let them grow.