To minimize the risk from falls or stumbles while hunting:
Never run or jump while carrying a loaded firearm.
Always unload your firearm when on poor footing such as loose rock and steep hillsides or when crossing obstacles such as fences or ditches.
Never try to cross a stream by walking on a fallen log! Find another place to cross or wade it if absolutely necessary.
Wear the proper footwear! Deep treaded hunting boots that give you good traction and ankle support are usually your best choice.
If you do stumble or fall, make every effort to control the direction of your muzzle so that it remains pointing away from you or your hunting companion(s). Open the action, unload the firearm and check for any barrel obstructions. Even a tiny amount of mud, snow or other debris in the barrel is extremely dangerous. Carry a portable cleaning kit and know how to use it.