I thought that this was one of the lullabies that everyone knew at least part of, like "Rock a by Baby." I guess it's not as well known as I thought.

I believe the song is usually called "Hush a Bye". The lyrics I recall are the ones that Peter, Paul and Mary recorded.

Hush a bye, don't you cry
Go to sleep, you little baby
When you wake, you shall have
All the pretty little horses
Dapples and grays, Pintos and bays
All the pretty little horses

Way down yonder, in the meadow
There's a lonesome little lamby
Birds and butterflies fluttering round its eyes
Poor little thing is crying 'Mammy'