However, all you get for it, at most, is an interest deduction on the mortgage and maybe some real estate taxes. That is not going to be much.
You will gain much more tax advantage if the hunting tree is used as a business. You could either guide, or lease it out unguided. Then, you can maybe expense or depreciate the equipment, building, tree, mortgage, and so forth. You can also maybe deduct those expenditures that you make to allow you to make money - mileage to get there, your guide's license, insurance, and so forth. If you have a working ranch and sell hunting leases, this is much better than a second home deduction.
Both of these ought to move you up many places in the "let's get audited by the IRS" sweepstakes. That is not one I want to win. I don't take questionable deductions at all.