One of the most striking aspects of Mormonism is the very positive attitude towards children - this comes through in official teachings by LDS church leaders, in publicity and evangelical material, in scripture, in LDS magazines and newspapers, and in the social statistics of Mormon behaviour.
The positive attitude towards children seems to be underpinned by two striking sections of the Book of Mormon - the delightful account of the risen Christ blessing the children in the book of 3 Nephi:
21 And when he had said these words, he wept, and the multitude bare record of it, and he took their little children, one by one, and blessed them, and prayed unto the Father for them.
24 And as they looked to behold they cast their eyes towards heaven, and they saw the heavens open, and they saw angels descending out of heaven as it were in the midst of fire; and they came down and encircled those little ones about, and they were encircled about with fire; and the angels did minister unto them.
...and the discussion of baptism in the book of Moroni, where it is very strongly asserted that the baptism of children is not just unnecessary, but an abomination:
12 But little children are alive in Christ, even from the foundation of the world; if not so, God is a partial God, and also a changeable God, and a respecter to persons; for how many little children have died without baptism!
13 Wherefore, if little children could not be saved without baptism, these must have gone to an endless hell. ...
15 For awful is the wickedness to suppose that God saveth one child because of baptism, and the other must perish because he hath no baptism. ...
17 And I am filled with charity, which is everlasting love; wherefore, all children are alike unto me; wherefore, I love little children with a perfect love; and they are all alike and partakers of salvation....
20 And he that saith that little children need baptism denieth the mercies of Christ, and setteth at naught the atonement of him and the power of his redemption.
However, the Book of Mormon was apparently not much used in teaching doctrine, and did not itself exert much of an influence upon Mormon doctrine, until relatively recently - so it is more likely that these passages are consistent-with Mormon practice, than that they are the origin of practice.
The characteristic, luminously positive attitude towards young children seems to be related to the Mormons having a different, and much more positive, interpretation of The Fall than do Mainstream Christians - and consequently their denial of the Mainstream Christian doctrine of Original Sin.
For Mormons, it seems that the concept of Original Sin is (to a significant extent) a denial of the power of Christ's atonement - and has the viscerally unacceptable consequence of damning unbaptized children (or, at least, that is how The Fall and Original Sin has been interpreted in much of Christian history - when at times children seem to have been regarded as something much like demons).
At any rate, the consequence for Mormons seems to be an attitude of great reverence towards innocent children, and a sense that they can be - by their example - the teachers of adults.
This fits with the idea of the family as potentially the most perfect Christian environment for adults; and contrasts sharply with other Christian traditions which see the ascetic, celibate monastic, nun or priest - or the subtle and profound theologian - as the greatest Christian exemplar.
(The Mormon ideal is, in fact, the most advanced actual form of the Via Positiva - the Way of Affirmation - among Christians.)
All of which fits seamlessly into Christ's positive attitudes and teachings with respect to children as displayed in the Gospels - which seems like something new, and something distinctive to Christianity; and an essential part of the sweetness of the pure faith.