Little children, yet a little while I am with you. Ye shall seek me: and as I said unto the Jews, Whither I go, ye cannot come; so now I say to you. John 13:33
[Middle] Eastern teachers, when conveying their love and closeness to their disciples, will address them as “little children”. Ecclesiastical authorities, when addressing a letter to the members of their churches, will write: “My beloved children [sons].” One also hears people engaged in conversation calling each other “my father” or “my son.” Elders usually address the younger ones as “my sons.”
Interestingly, according to custom, people call or address unlearned men, no matter how old they are, as “little children.” When God called Jeremiah to preach to the people, the prophet said: “I am a child.” This means “I am unlearned.” In Arabic, people refer to such person as jahil, “inexperienced.”
(Errico, Rocco A. Let There Be Light, Noohra Foundation,
We see this particular usage of "little children" as well in D&C 50:40-41. Joseph Smith certainly was inspired, because this is not a typical (or respectful) way to address grown men in American culture.
40 Behold, ye are little children and ye cannot bear all things now; ye must grow in grace and the knowledge of the truth.
41Fear not, little children,for you are mine, and I have overcome the world, and you are of them that my Father hath given me;