I can't speak to deer, but my cousin had an elk farm previously so that was at least legal. Given concerns over wasting disease, I'm not sure if farming deer would be a good or bad idea - as in, do we end up with a concentrated population that might spread the disease faster, or do we save the species by separating it from their wild cousins?

Often complicated, rather than illegal. https://worldpopulationreview.com/state-rankings/deer-farmin...

While driving through Texas after the total eclipse, my wife and I were reading about the high fences on Texas ranches (deer hunting ranches, possibly with managed breeding), and enjoyed this article on the tradeoffs https://www.texasmonthly.com/the-culture/which-side-of-the-f...