There are some houses to rent within walking distance or a short drive to the showgrounds. El Soto is the area to search if you want to be beside the showgrounds (most houses are simple). The village of Vejer De La Frontera is about a 10-minute drive away. Houses and apartments are available here and within walking distance of some excellent restaurants. Check out air B&B too.
The very helpful show office also has a list of rentals in the area.
Most if not all houses and hotels are built for hot weather and can be cold and damp so bringing some hot water bottles or an electric blanket is a good idea.