Congratulations on buying a house there! I sure wish we could...
My family goes off to joshua tree maybe 2-3 times a year. And we did go hiking in 114 before :P

Have you really never seen ocotillo there? In joshua tree national park, there is patches full of nice mature specimens, probably 15'+. Ive also seen giant red barrels, and mammillarias around there. Ive also seen acacia growing wild, here and there. There is also giant patches full of very large golden cholla, maybe around 7 feet tall.

Yes, I have seen ocotillo in JT, but there is none growing wild in my immediate microclimate.

Opuntia are a large genus. Maybe some arborial opuntias that can take some feeze. O cochinellifera and O. leucotricha can take some frost and are water tolerant in the cold , I think. They might need more drips in the summer. Every 3 weeks is sufficient . but get that drip system so one isn't watering your whole vacation. There are so many cool opuntias. I have 68 varieties. Cylindropuntias are really cool too. I habve never been to the JT areas but I know they are native to Southern California and Arizona. Cylindropuntia Fulgida will add some height. Jumping choll does cool things by glimmering in the light.

How cold does it get on the winter nights?

Winter averages are a high of 60 and low of 40. That happens from December to March. April and November are 70/50. May and October are 80/60. Rest of the year is 90-100 and a low of 70.

Record low is 15, but under 30 is pretty rare.

Iy sounds like a lot like Austin Texas but with less moisture and maybe our record is lower.We sure don't look like you so something has got to be different. LOL.

The humidity, I am sure, is one huge difference. The Mojave has none except during occasional summer monsoons. Occasional meaning once or maybe twice per month.

The Mojave desert is very, very dry. The average is 2.5 to 6.5 inches of rain per year and when it gets more than that it tends to fall at once. That doesn't mean there aren't wet years where it might get 30 inches but that's uncommon. In general it is much drier than the Sonoran desert of Arizona. I have read rainfall is about half of the Sonoran desert, which is why plants like saguaros which *should* otherwise like it do not grow natively. However, with occasional irrigation they do very well.

Another difference is the elevation. Austin is only about 500 feet over sea level, whereas the Mojave is 3000 feet+.

Well, I had figured that much out. Rainfall is a biggy. A year ago I had 5" of rain from september to september... Our plants or land are not designed for it.. I am at 1395 above see level . The land goes up West of austin . We get our rain all at once too. I am always amazed by similarities and differences. It does not take much to totally alter a landscape. How rain is delivered. We seem more arid because our rain comes in large lumps and flows fast off our hills. We cal have a 7", a3" rain and a day later there is no mud. We have the same rainfall amount as lush Seattle and Sequim Washington.

If you find interest in annuals and perennials, the deserts are known for their spectacular bursts of color after a wet spring. I live in the central valley, and am growing several natives from the deserts south and east of us. Left to fend on their own, they are quick to bloom and set seed, but with a little irrigation, you can keep them blooming longer. Some of the ones that come to mind are Penstemon Barbatus, Penstemon Pinifolius, Gilia Subnuda, several delphiniums and Agastache rupestris. There is a great variety of plants you can choose from, but it will be difficult to find them at a nursery. You may need to find a seed source and grow them from seed yourself (that is what I had to do.) It's fairly easy and fun! Good luck!

*I can't post the names of the seed companies i purchased the seed from, but if you shoot me an email, I'll forward you the page.