A tangle of spider webs inside your home is usually a strong indicator of air leakage. Spiders travel on moving air and build their webs where there is plenty of insect activity. This usually coincides with gaps and cracks in your thermal envelope. As air leaks in, spiders have a highway into your home – along with other critters. Finding these spots of concentrated insect activity will give you some insight into holes that you can seal to improve your energy efficiency.
Your thermal envelope is the system that separates conditioned from unconditioned space. Your thermal envelope should be air tight and vapor permeable in this Mixed Humid Climate. Having a hole in your envelope that allows spiders to infiltrate means you have a huge air leak and this will impact your indoor air quality and energy efficiency. Think of it this way, if you have spider webs, the spiders are doing you a huge favor by showing you the weaknesses in your home so you can address those areas immediately. Rather than spraying or stepping on them, perhaps you should shower them with gratitude for helping you save money (or maybe just spare their lives and carry them back outside).