First off to those that have suggested replacing the entire fenceline... Do you have any idea the cost involved in replacing 160 acres of fencing? WOW!
Second, the ones that suggested a smaller fenced in area of 3-4 acres with either wood or electric are probably the cheapest route for fixing it because as Kevin said, she may be one of those fillies that is going to figure out how to hurt herself even in the safest, cleanest environment...
Next, are there cows in or around this pasture? If there are cows involved then the barbed-wire is the safest route for the cows. The safety of all animals involved needs to be considered in this scenario.
The ribbon idea is a good one because it may be a matter of her not paying attention to what she's doing. Also, as many have stated Barbed wire can be a safe fence IF it is installed properly. Which means the entire 160 acres needs to be walked/driven on a regular basis to ensure it is taught and no loose peices are laying around.
And last... I like the bubble wrap idea!