The sons of Kohath were given holy things to carry. Aron and his sons were asked to take the ashes from the altar and spread them on a purple cloth and then place the firepans, forks, shovels, basins and all the other utensils present at the altar. They were then asked to cover the sanctuary. Now the sons of Kohath had to carry these sacred things but not touch them as they could die due to this sin.
Furthermore, the sons of Kohath were not given any horses to carry the things as the holy utensils were meant to be carried on the shoulder.