No you can not go out and catch your horses, as they are your property, but it is a racket.
For a bit of history and advice.
These are not mustangs. These are crossbred horses of American horses which escaped and interbred with the "mustangs". The Indian horses were so horrid that Col. Charles Askins used to shoot them for his pack of hounds back in the day. The best purpose for them was then pet food companies rounded them up and killed them for food.
My friend and his father who was a deputy sheriff, obtained 3 of these things. They literally climbed the walls of the barn, they never could do anything with them, and eventually sold them, which meant they were slaughtered. I strongly suggest that you look online as there were sites in people who attempt to train these animals. They built wood holding stalls higher than they could jump out of for starters. One guy had a castrated old stud, and the only way they could do anything with him, was the wood chute as that is the only place the animal would feel secure. The cattle out west are going "mad" because wolves and mountain lions are driving them that way. These mustangs are hunted by large predators and survive by being this wild. I read of a gal in Montana who had a "pet" curly stud, who one day decided to do what studs do and bit her hand, crushing it.
Most of these horses are small and inferior. If you read the history of the way Indians broke these animals in George Catlans journals, they would run these animals to ground, meaning exhaustion. Once they had them down, they would breathe into their nostrils, get on them and ride them to more exhaustion. It does not seem humane, any more than the other method of shooting them in the neck with muzzleloaders to stun them, but that is what Catlin wrote of, and mentioned a Comanche chief who was riding a stud horse, a Spanish bit had it bleeding from the mouth, and he had Mexican spurs on, and would jam them in, the horse would go wild, the chief would laugh and gallop across the plains. All that makes a person cringe now, but that is the history of this animal. They ate cottonwood bark and were abused.
There is a very good book by an American trainer that is free online from the 1800's. He had a method of roping and throwing horses to train them. There is a difference between training, gentling and breaking a horse. I have trained horses and while there are exceptions to the rule, I would advise not dealing with these animals. Teddy Roosevelt in his Ranchman and the Hunting Trail gave some statistics in if he purchased 20 horses, about 15 would either try to kill you, continue to buck or run off. He had two good horses on his ranch, one was too small and the other was an Indian trained horse he called Manitou.
If you are still wanting to do this, get your health insurance paid up, never trust that animal and never forget it was wild. You may get the 1 out of 1000 in a suitable horse. I hope it turns out for you, but there is a reason the federals had orders that people could not sell these animals, and that was because no one could handle them, and there is reason they are trying to sucker people into taking these horses, as no one wants them from past experience.
If you are looking for something to give you problems, just buy a Poco Bueno descendant, as my neighbor has one which bucked off his 70 year old dad and broke his shoulder, and I have a red roan who has attitude like a woman scorned. That is from the Quarterhorse line of race horses.
Lastly, quality hay is 35 dollars for grass and over 100 for alfalfa. 500 dollar from the government disappears fast and the 500 dollars for keeping that mustang past the first year in a second payment disappears as fast and the key word from the BLM is THE LIFETIME OF THE HORSE. What are you going to do if you have to keep that animal for 20 years, it turns out it is dangerous to people, and you have the BLM and Humane checking on you, inquiring why you are abusing that horse having it locked up all the time, because it keeps tearing through fences and you can't catch it.
There is nothing free in life and 18 years of feed at 500 dollars a year is 8000 dollars, plus the insurance if you mustang gets loose and hurts someone.
https://www.cbsnews.com/news/bureau...-you-1000-to-adopt-a-mustang-wild-horse/So BLM did some simple math: Rather than pay $2,000 to care for a mustang for one year, they'll pay $1,000 to someone willing to adopt and care for a mustang over its lifetime.