Tai Chi Walking: Note what Master Hwa says in this video at the about keeping the head up, not watching the feet. Now take a look and scroll to 2:45 of this Brain Fitness video
Youtube link and you see what can happen when watching the ground while walking. Note the methodology that is employed in "internal discipline" of walking, how one lifts the pelvis which really offsets the body to first one side then the other...but how this ingenuity of training acts to improve balance. The caveat here is that one first must learn where they are unbalanced to learn how to balance themselves. This type of walking is not everyday walking where we move by an act of "controlled falling" through the constant movement and putting one leg in front of another...this is far from it, everything is under control and command from the core.
Student's may struggle in the beginning to not watch the feet or ground. Just as in learning to keep the weight back while basic walking, this requires patience and consistently reminding oneself to keep the gaze up. It is the kind of practice however, that one can integrate into daily activities. It can be "practiced" anywhere/anytime and is called "offline" practice. If you will see p. 68 of Uncovering the Treasure you can see the encouragement that Master Hwa offers in this endeavor.
He says: "The advantage of (offline practice) this is not only to have more time to practice, but also to get used to the idea of incorporating internal moves into everyday life. The other advantage is that such offline exercise is carried out in a casual and relaxed mood with more of a chance to let the subconscious play a part. The objective is to learn internal moves piecemeal and then integrate them into form play".
He speaks of offline practice as being a means to learning internal and this "keeping the head up" falls well within that "internal move" category. One actually learns to right the head not only subconsciously but learns to do it from the core of the body.