Is it recommended for a man to cover as much of his body as possible, following the example of Musa (عليه السلام), who was modest and concealing, so that nothing of his skin was seen?

A man is required to cover his awrah, which, according to the majority of scholars, is the area between the navel and the knee. It is commendable for him to cover more than that, as is customary among honorable people in his locality. Exaggerating by covering the entire body is not a virtue, as the Prophet, peace be upon him, did not do so. The story of Moses, peace be upon him, covering his entire body ("nothing of his skin could be seen") means that he did not expose himself to others while bathing, not that he covered his entire body in all circumstances.