Spin her in a tight circle everytime she tries it x
There are several options:
The first and most simple is to drop one rein and turn her in a very sharp circle. It works a lot of the time, but I've also had one particularly stubborn pony continue to run blind, despite his nose being at my foot (yay for ponies!).
I'm a "start with nothing, add as much as needed" sort of person when it comes to all aspects of horses, including tack. If your bit is not strong enough, there's no harm in getting a stronger one if needed, as long as you have soft hands usually.
I'd start establishing your stop/start response in the arena too. Make sure it's as snappy as you can make it there, and it's more likely she'll stop out in the arena. Make stopping a positive experience and start with ground work. I recently made a post here about groundwork, if you'd like me to link it to you?
Do you ever walk her in hand along your hacking routes? Does she do the same then? If she does, or if you've never tried it before, it might be worth doing. Take a schooling stick with you and if she tries to run off, turn her in a circle. If she still tries to go, despite being on a circle, it's okay to use the stick in front of her to stop her.
The idea is to make running away less desirable and walking normal more desirable. You're right in that what she's doing is dangerous, not only in bad footing but you just never know what she's going to run into/jump over. It sounds like a bad habit, so it may take a time and patience to stop. It might be worth having a rider on her too that has had experience with horses taking off.
We had an older horse who used to take off solely because it mean someone would stop him and he wouldn't have to work. It was a very clever technique really, because your first instinct is to stop a horse that's bolted. Luckily, this was only ever in an arena so what we did was push him on and make him canter for a lot longer that he wanted to, every time he "took off". He eventually stopped because he wasn't getting his way any more. Although that particular technique wouldn't work for you, it's the same concept. You make what they want to do unpleasant so they are more willing to do what you want to do instead.
You should do a lot of transitions like walk to trot sitting trot walk to canter etc.