Do electricity prices vary throughout the year? I don't remember that being the case when I lived in the US, and it's not the case in Ontario. We have time-of-use pricing that swaps the mid-peak and on-peak rates, but that doesn't affect the total charge very much.
Utility companies offer a product of supply and demand. During the middle of the day in the summer in Texas, demand is at its peak as everyone runs their A/C full tilt. That's the most expensive unit of electricity, so the pricing reflects that. Everyone knows that you don't run your laundry/dishes during that time. Winter time, most places are heating with gas, so electricity demand is just never as high so the prices are cheaper. Yes, some pricing options claim they are giving "free nights and weekends", or avg billing that "lowers" the summer rates while "raising" the winter months to keep it on average the same per month. That doesn't actually change the rate per KWh at the time. It's like buying car with the squeezing the balloon analogy, squeeze the price on one end the numbers bulge somewhere else.