The two biggest challenges you'll have to get used to are :
1. Learning to hunt in hot/very humid weather. I know it can get hot in NM, but at least the humidity is low. During archery season here it is almost unbearable.
2. Getting used to the idea that you cannot just walk through an area and stand a reasonable chance of seeing game (meaning deer and hogs). Even if you have an area with some open terrain, our animals will avoid that in favor of the thick stuff. They can move through the thick stuff but you can't - at least without sounding like a herd of elephants. That is why treestands over game trails are the norm here.