I wear chaps all the time and I'm certainly not a cowboy, nor do I play one on TV.
That being said yes, chaps will help you "grab" the saddle a bit better, which is why I wear them as well as being wonderful in deflecting brush (and for you you perhaps cacti?).
Some thoughts to consider
Full length (shotgun or bat wing) chaps will certainly protect your entire leg from brush ect. But can be very warm, after all you're encasing your leg in leather. They are also heavy and hot - if you want the look you've got to pay the price.
Short chaps (chinks) will still give you the extra grip but lack the lower leg protection from brush / rain. They are however much lighter and cooler.
Leather or other materials - leather is certainly traditional but it is heavy and contrary to popular opinion is not waterproof. Great for light rain but it will soak though in time. Oilskin is waterproof and also quite durable but doesn't have that "look" if you will. Good quality leather chaps are also spendy.
I wear chaps of some type throughout the year. Oilskin is generally my first pick (but I live in a rain forest, Seattle gets wet!) and switch over to leather chinks for the whole 6 weeks of summer that we have.
If you visit the Texas page of www.trailmeister.com
you'll see on the right hand column an ad for oilskin chaps that have a traditional look to them.
The "TrailMeister's" $.02