If I’m on differed probation for a felony but still want to hunt deer, can I own a muzzle loading rifle or handgun?

Under Texas Law-- you are not considered a convicted felon for purposes of owning or possessing a firearm.  However, under federal law.... you would be considered a "prohibited person" because you are still subject to an indictment.  This means that under federal law, you would not be permitted to own a firearm.  Even if the state chose not to prosecute you, the feds still could and the fact that your possession under state law may be legal-- will not excuse the federal charge.
Once your deferred probation is completed, you can possess a firearm under either federal or state law because you would no longer be subject to the indictment.  You can risk possessing the firearm, but know that the risk you are taking is a potential five year commitment in a federal prision.  The better solution would be to finish your deferred probation.  Texas does have a provision which allows you to obtain an early discharge if you have completed all of your community service hours and paid your fine/restitution.  The timing on when you can get off will depend on your performance-- but if you have done well-- you can get off in a third or half of the time depending on the nature of the underlying offense.  Take your plea papers to a criminal defense attorney and ask them to review them to see if /when you would be elible for an early discharge.