Common misconception. People wore 'heavy' armor in the desert all the time. It's the point of a surcoat.
It is worth noting, however, the Spanish did tend to decrease their armor use in New Spain (e.g. Mexico) -- I'm speaking from researching the 16th century, but it likely holds true for later periods. The explanations I've read indicate this was due to decreased benefit from the armor (primitive native weaponry) combined with increased cost of use (it was often pretty warm).
One change you will need to make compared to the typical Northern European mindset is that the campaign season for the typical 'Zorro' type locale would be continuous. If it does break, it would be centered on the winter, not the summer. Weather and climate is crucial to warfare at these levels of technology (and it's nothing to ignore today), so given the choice, generals will campaign in the fall through early spring and avoid engagements in the middle of the day.
Logistically, campaigns would pay lots of attention to water and salt. (This was still true at least until the US Civil War. Look up the Battles of Saltville I and II.) Not that medieval European generals ignored these, but they take on extra imetous in a warm arid environment.
Southern California climate patterns have most of the rain falling in the winter. The driest period, in terms of water availability in streams and such, would be autumn. You could expect the same patterns in Baja California (the peninsula at the northwest of Mexico) and northwest Mexico. As you head east in the southern U.S. (and, presumably, the same holds true for northern Mexico), you pick up summer monsoons resulting from the influence of the Gulf of Mexico. In all cases the summers are hot.
Assuming you're using regular soldiers (and, therefore, don't have to worry about pulling irregulars from their agricultural duties) I'd campaign in the winter and spring. You could continue into summer if you had to, but that would suck.
Miscellaneous California agricultural stuff...
I can't speak for the rest of California, and this is from memory, but the Spanish came into the San Bernardino valley (Southern California, perhaps 70 miles inland) in the early 1800s. With the "assistance" of native laborers they began irrigating parts of the valley. I have heard some suggestion the primary canal dug by the Spanish followed, in part, pre-existing native irrigation routes, but haven't seen any real confirmation of that.
Citrus didn't become a part of California history until the late-1800s -- it was in the 1870s (?) that navel oranges were sent to Riverside, CA, sparking a "second gold rush."
Walter
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