I have super dry skin, and I do use a certain few primers that are known as "Hydrating Primers". I agree with what makeupbyomar said above, that primers won't necessarily hydrate your skin, but you can find some that won't be especially drying or siliconey and thick feeling on the skin. Basically, they won't exacerbate the dry skin situation on your face, lol. Here are my top picks:
Laura Gellar Spackle Hydrating Primer (My personal fave that I use every day. It dries a bit tacky, so you know it helps your makeup adhere to it and last all day)
Too Faced Hangover Primer (This has coconut water in it, which is naturally hydrating)
Glossier Priming Moisturizer (This is like a moisturizer and primer in one, so if you are using a really good moisturizer, which I highly recommend, then adding this on top will give you really well moisturized skin)
I've also heard, on the drugstore end, that the Nyx Honey Do Me Up Primer is pretty good for dry skin too, and have been wanting to try it, but haven't had the chance yet. It seems like it would also give you a nice luminosity to the skin.
P.S. I'm sure you already know this, being a fellow desert skinned gal lol, but a primer should never replace your moisturizer, even though these particular ones that I mentioned will feel very hydrating and moisturizing to the skin. They will dry down and create that smoothing barrier for you, so that your makeup will look flawless, but they won't actually sink into the skin to give you what you need, as far as deep hydration goes.