Young mesquites are trying to take over my friends ranch. Are there any exotic goats or something that will really eat and hopefully kill young mesquite trees?

Nothing kills mesquites. When we are all extinct and there is nothing left in the world there will be 3 things. coyotes, [censored] roaches and mesquites.

You censored a roach? Wow

A root plow is the best way to kill mesquite.

A root plow is a great way to spread mesquite.
Spraying often is the only way to kill. And you need a pocket full of cash.

Someone needs to genetically alter a goat so that it will only eat cedars and mesquites.

Will a copper nail kill mesquite trees? We used to use them to kill old rosebushes.

4. You forgot bermuda grass, nothing will kill it either!

I noticed mesquite seedlings coming out of the rain-soaked cow patties at our place this past weekend, so I'm going to infer that animals eating the mesquite seeds are actually helping to spread them out, thus resulting in the apocalyptic scenario described above!

Mesquites are amazing. You lop a young one and 20 more branches sprout from it next year. It's natures little miracle.

Goats will eat mesquite and cedar. Eating the leaves off a mesquite will not kill it. Goats will eat the green leaves and the bark on cedar. If it is a small cedar and they eat all the leaves the cedar will die. But to do this you would have to be way over stocked on goats.

camels

The man that does invent a mesquite/cedar eating exotic will be multi-millionaire.

Hydroaxe

What about mosquitoes?

Absolutely. Folks ranched when i was a kid, back when we hunted dinosaurs with stone tipped spears, anyway we had a small patch adjacent the corrals, any animals coming on to the place stayed in that small patch for a couple of days to slow the mesquite spreading.

The cattle drives of the 19th century did a lot to bring mesquite to every corner of Texas.

Depending on what young is and how many and how large a property you can do a lot with some time and a pump up sprayer or atv sprayer.

after root plowing it can be controlled with annual spraying

Supposedly, cut it as low to the ground as you can, mark an X in what is left and pour salt in the X and around the base. Not sure how many times you need to put salt on it but I think maybe two or three times if you don't see any results from the first dose after about a week to ten days.