Joe,
A Google search turns your original verse up in an anecdote about a WWII RAF pilot.

My older brother, Andrew, was a pilot in the Royal Air Force during World War II. At age nineteen he was facing death every day. He would return to base sometimes with an engine or two shattered. On one raid his co-pilot, Gregg, was killed at his side. In these early days of telecommunication the pilots had to speak into the intercom. as they came close to base, so that they could be traced and guided towards a safe landing. So they kept repeating things, poetry they had learned at school, newspaper headings, anything. Andrew told me once, shyly and with some embarrassment, that the call-in lines he most used were these:

I don't care if it rains or freezes,
I am safe in the arms of Jesus.
I am Jesus' little lamb,
Yes, by Jesus Christ I am.

From:
Sermon preached by the Rev'd Dr. J. A. Ross Mackenzie

St. Luke's Episcopal Church
"Good Shepherd" Sunday: May 6, 2001