Your mare will benefit from working on proprioception; something I work on with all my horses. Some are born knowing where their feet are - they tend to be the more hypervigilant, “careful” types (though that’s a generalization), others not so much, but they will ALL benefit from exercises to improve this.
What bfne suggested is good: scatter poles around and have her figure out how to negotiate them at walk and trot without rider input (just stay balanced, keep your leg on and give her the rein to stretch down when needed), but cavaletti spaced for walk, trot, and canter distances will also help her - and all horses! When she learns to be more careful, raise them off the ground - they should be ridden in a steady rhythm with a stretchy, long neck and elastic connection.
I have done a lot of TTEAM exercises with my horses when young (or rehabbing); the labyrinth is excellent to improve balance, and helps calm the horse and activate the “thinking brain.”
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The star pattern is also helpful - I raise the ends of the poles and vary the distances (you walk them through in hand), and this really compels the horse to pay attention to where she is placing her feet! Take your time, let her process.
I also like to back the horse over poles (also in hand) step by step, and also work on backing up (in hand) in a slight shoulder-in position. Backing them up gentle hills in hand strengthens the core and hindquarters. Just make sure the head is down and the horse is engaging the core and “coiling the loins” and not hollowing, raising her head, and rushing through while dragging the hind feet - you want deliberate, careful steps.
When riding, lateral work in walk is extremely helpful (TOF, TOH, S/F, S/I), as is working on halting with “a leg at each corner”, gentle stirrup stepping into each hind leg as the horse comes to a halt (“halting into the hind legs”) will help the horse balance herself off her shoulders and develop awareness of shifting the weight back and over all four legs.
Walking over poles in hand, you can halt the horse at various moments with feet between the poles and stand her there for 10-30 seconds so she can “process” where her feet are.
Another exercise I do occasionally is put up a line of about 6- 10 poles and “weave” the horse over them; stepping left over then, then right - using your legs and gentle weight aids to shift the horse back and forth will help you use less rein.
Obviously walking horses over varied terrain (and up and down hills) on trails AND setting up gymnastics, bounces, placing poles, etc. in the ring will all be extremely beneficial.
It takes time to improve this in a horse to whom it doesn’t come naturally (think months), but the good news is that if done consistently, a little will go a long way. Doing 15-20 minutes of the above exercises 3-4 times a week will really pay off down the road.
Best of luck!
ETA: often when horses trip on trails or hacks it’s because they aren’t paying attention (IOW “sightseeing”), hence not paying attention to their feet 😉 In these cases it’s helpful to halt, move the feet around a little (lateral work, TOF in motion, a step or two of reinback) to get the focus back on you, then continue…Rinse repeat as needed.
