I know zip about formal learning theories, but as someone who both plays and has taught piano, has long ridden horses and taught riding, and is a brand new adult learner to figure skating, this is an interesting question to me. I have taught both adults and kids in piano and riding, I strongly feel that adults incorporate new material differently than children, one of the biggest differences being the "why" of the matter. Kids can learn the technique first and tend to start understanding why the technique is the way it is at a later time, while adults will often want to know the reasoning behind techniques up front, it seems to help them pick things up more quickly.
To me teaching riding is much closer to learning to skate than teaching piano. Teaching piano is like teaching someone another language that they not only have to read and write, but that they must express that written piece through a physical movement (that muscle memory again) and they must train their ear to hear if what they are playing sounds right. They use all of these senses very intensely to play beautifully, and it is complex. Teaching riding and skating at least in the lower levels, seems more physical, and with physical stuff you have the above listed learning patterns of the tentative first steps, the more confidence building second step steps and the third steps of muscle memory being built. And as an adult, learning the "why" reasoning behind physical steps helps me.
The piano though....when I teach, I teach the person to read, write and play music all at once, in addition to listening to what they actually play. I think their listening is the most natural evidence of perhaps genetic type talent...some folks are able to listen from the onset and knew that something sounds wrong, others never quite get there, they always rely more on reading the music correctly. Truly experiencing playing music is a combo, IMO. But people will have strengths in certain areas just as with skating elements. Music learning with adults in particular is typically a slow process, but it teaches them correct counting, and fingering that will be used even in the highest levels of piano. I try to make my students have something new and enjoyable every lesson, a fun little relevant song to learn along with the other work, something to show what good can come from learning the more boring and sometimes frustrating theory and sight reading.
That said, my goals as a skater is in ice dancing with hubby, and I am hoping my musical counting and timing will come in handy with the steps, it has when I have done other types of dance on the past.
As a nurse by profession, I have experienced and observed the novice to expert transition that all new nurses make and they go along with standard learning theories described by many. I am often fascinated by the idea of innate talent in general. For instance, just as some have a tendency to hear music more effectively from the get go, some new nurses make clinical judgment decisions easier than others. Even when their experience is less, they may simply see nursing decisions as very much like common sense whereas some other nurses are pondering the issue, just not able to come up with an answer. It is fascinating how our individual brains can simply work better on some subjects than others.