Jamieson, Fausset and Brown on Leviticus 10:6

6. Uncover not your heads--They who were ordered to carry out the two bodies, being engaged in their sacred duties, were forbidden to remove their turbans, in conformity with the usual customs of mourning; and the prohibition "neither rend your garments," was, in all probability, confined also to their official costume. For at other times the priests wore the ordinary dress of their countrymen and, in common with their families, might indulge their private feelings by the usual signs or expressions of grief.