I was just going to post a link because I thought it was a pop/country song. Looks like I was wrong, although I'm not convinced it's really traditional. Apparently, Loveless sang it on the soundtrack of the fascinating Robert Duvall movie, The Apostle.
Also recorded by Ralph Stanley, Blue Highway, and the Dry Branch Fire Squad.
-Joe Offer-

Two Coats
(Traditional, Arranged By: Emory Gordy, Jr., Patty Loveless)

Two coats were before me
An old and a new
I asked my sweet Master
Oh what must I do

The old coat was ugly
So tattered and torn
The other a new one
Had never been worn

I'll tell you the best thing
I ever did do
I took off the old coat
And put on the new

The first man was earthly
And made from the ground
We bore all his image
The whole world around

The next was my Savior
From heaven so fair
He brought me this new coat
You now see me wear

I'll tell you the best thing
I ever did do
I took off the old coat
And put on the new

Now this coat is suits me
And keeps me so warm
It's good in the winter
It's good in the storm

My Savior has dressed me
In a garment so rare
He brought me this new coat
You now see me wear

I'll tell you the best thing
I ever did do
I took off the old coat
And put on the new

I'll tell you the best thing
I ever did do
I took off the old coat
And put on the new

source: http://www.sing365.com