The text for the first verse is
He's got the whole world in His hands,He's got the whole wide world in His hands,He's got the whole world in His hands,He's got the whole world in His hands.
The first three "whole"s are sung to half notes, and the difference between the lengths of these half notes and the much shorter values of the surrounding notes provides a sense of that entirety. The first three "world"s are each sung with a melisma (A F, G E, A F, respectively), and this gives a sense of the breadth of "whole" and "wide."
Each verse simply substitutes something else for "the whole world." The second verse alternates between "the wind and the rain" and "the sun and the moon"; the third verse repeats "the tiny little baby"; and the fourth verse alternates between "you and me, brother" and "you and me, sister." To some degree, then, the text is a rhetorical catalogue, listing various entities that are "in His hands" and indicating the all-encompassing nature of God's care.