This is what I thought! I am right side dominant and suffer from dry hands and feet mainly on the right side (with a slight numbness in sensation on the feet, nurse doesnt think there is damage there though), my muscles on my right leg are also weaker (collapsed arch - when doing the strengthening exercises I notice it). But I took that to be wear and tear because of the right dominance... (plus I have an old knee injury on that side, so I am sure that factors in somewhere...).
I have hard skin under my right foot, which is sadly getting worse... But I also have more of a collapsed arch here, so my foot may be moving in such a way when I walk that the skin is rubbed (is it called pronating?). Are your arches all normal? When you stand do you do the penguin feet or do the toes point out straight? My physio noted straight away that my right foot points outward when I stand. Maybe I am part penguin?