Yes, very few covereds around. I was horse hunting in that area this past Summer. And I had a horse boarded out there the Summer of '16, so I got to ride out there myself then as well as to audit at some big-name places.
Nowhere did I see or ride in a covered dressage arena, with the exception of the facility that Absolute Equestrian mentioned above. And I tried horses and audited lessons at seven or eight different stables in the North San Diego area (including at Arroyo Del Mar, Albert Court, Ad Astra, and Seabreeze), as well as facilities in Temecula and in Orange County.
Those places just didn’t have covered arenas. The trainers based there all seem to get the job done, and the footing in the outdoor arenas included some of the best products available. They do lose some training time day-to-day when they’re hit with a lot of rain, and I remember hearing that rain was a factor in the cancelation of a Southern CA show this past Spring.
So it can be an issue, but apparently it’s not a regular occurrence because many of those places have the $$$ to install covered arenas if they felt they were needed. If I were looking to move there I don’t think I would include a covered arena on my list of criteria because that would severely limit the boarding-stable options.