People seem to think the mid-mount Zero Turn is the only style of Zero-Turn there is which I agree will flip over backwards going uphill. They are kind of like an old M or H tricycle style they tend to flip themselves with the torque in the drivewheels going uphill.
I stated my "front deck" zero turn will not flip in any direction. If you want something for a steep hilly area that is truly safe get a front deck Zero-Turn machine. Mine is a Deines but Grasshopper, Woods, Deere, Toro, and a few others make them. The only dangers you have is losing traction and sliding somewhere you do not want to be or sliding out of the seat with no seat belt. My true preference is a Grasshopper or Woods because the lower center of gravity and ease of mounting and dismounting but it is not what I have. And while Indiana is not known for its steep slopes there are plenty of places where developers put in some steep slopes as they graded their building pads or in my case a pond bank. And yes I have slid down a few of them and it can be a little exciting but no injuries or damage - I did get very wet one time though.