We hunted Barbary in southern New Mexico in January a few years ago.
I don't know what the temps will be where you are going, but the cactus and shin-dagger thorns should be pretty similar... and they were terrible.
We wore heavy boots with ankle-height gaiters to keep thorns out of our socks. It was too warm for heavy pants or chaps, but we found the KUIU Tiburon pants were more resistant to thorn snags than the KUIU Attack pants.
When I go back down, I'll take long underwear to wear beneath Tiburon or Alpine pants in the morning and then take the long underwear off as it warms up during the day.
Have fun on your hunt, that's on my shortlist for the next few years. Let us know how it goes.
Grizzly