Robertoalan, I looked at your profile, and I noted the fact that you‘re not actually in the military, so I don‘t get the fun of calling you down as a poser.
Allow me to explain a few things (And this is for you too BDTyre, since you asked the question).
With regards to running outside in the winter, yes, somone will have made sure the path is clear. No one in charge of a PT session would be so stupid as to take their troops outside to run on ice... people would be slipping and falling and injuring themselves, and responsibility for these injuries would likely fall on whoever was running the PT session.
There are a lot of inherent dangers in military service, in garrison, in the field, or deployed... that being said, safety is always the foremost concern at all times.
Think about it, an injured troop can‘t train, can‘t fight, can‘t do their job. The military is also responsible if any permenent injuries result.