Trouble with renting anything is that at some stage the owner may need you to leave. In terms of your proposition, to start a deer park/farm, you would have to spend a not insubstantial amount of shekels on fencing, not to mention your animals and everything that goes with them.
Imagine that you get everything in place, fences are up, your beasts are in, then the land owner dies/sells up/decides he wants his daughter to keep her ponies on it....
At that point you suddenly have deer to be moved somewhere else, fencing to either take down or leave behind at a loss.
That's when you realise that renting is a risk, and so not really viable. Even if you didn't have to move, the feeding over winter, potential vet fees, fence repairs and the likely loss of animals that go with a downed fence would make your outgoings prohibitive.