Mesquites are an every day thing here on my ranch.
When you replace the tires, get 6 ply and run slime in them.
After a while, the slime will start to dry out so you just shoot in a cup of antifreeze in there and you are GTG.
You can get a decent set of 4 6ply tires off of ebay for under 300 bux a set delivered.
I had a set of essex on a mule and loved them but they came on it - I can't see paying 2-3X for essex anymore.
I picked up these off of ebay for 288.00 delivered.
They are 6 ply and have tall knobs so a lot of the time, the thorns don't reach the tire body.
They are a lot smoother than the chevron tread mudders I had on there.