I live in TX and own land in OK. Two different states, two ways to deal
with the high fence issue. Most places in TX bring in outside genetics and raise deer, some in small high fence places. But most are large acreage properties where the fence is more a deterrent than an enclosure. All normal stare hunting regs and seasons apply and deer and animals inside are still considered state property even if you bring the deer in from other places (you bought the breeder deer). The main reason people put up high fences in texas is to attempt to control the deer herd and/or prevent neighbors from shooting deer, as there are many small ranchettes in TX.
In OK, the stare requires you to leave a portion of the fence incomplete, and then the state does a drive to attempt to rid the property of all the native deer, at which time you can close the fence and then whatever is in the fence or whatever you bring in is essentially yours to do as ypu please. Hunting regs dont really apply but there are rules about record keeping and such. But you own the deer, and you can hunt them anytime. The main reason people high fence in OK is to control the herd and be able to gun hunt a longer part of the good hunting time.
Of course commercial hunting Operations use high fences to create an easier hunting situation for both states.
This is my meager undersranding of the high fence issue in the two states. I may be wrong on some of the issues, so dont take my words as gospel truth.