Yay! My research thus far. The Colonization title followed by the original title. I'm guessing 100% of the soundtrack is based on actual music. What's surprising is how much of it is based on Appalachian tunes... which, I suppose, might be the successors to old pioneer songs?
The only one of these that I'm not absolutely sure about is Little Fiddle. It seems to me that Shove the Pig's Foot Further into the Fire was probably the base tune here, with some heavy modification on the part of the Colonization sound mixers. But it might be wishful thinking.
Bird Song: The Bird Song (Lesley Nelson-Burns)
http://www.contemplator.com/child/birdsong.html
Smokey Tune: My Home's Across the Blueridge Mountains
http://www.youtube.com/watch?v=8Ww3IY84Op4
Cornwall: Cornwall (Albert d'Ossché)
http://www.youtube.com/watch?v=iwQN32m2K4s
Shady Grove: Shady Grove
http://www.youtube.com/watch?v=b-kaG1NuLZM
Fiddler's Dance:
Jine the Cavalry: Jine the Cavalry
http://www.youtube.com/watch?v=HDq09oSt9o0
Joe Clark: Old Joe Clark
http://www.youtube.com/watch?v=gKAtLiKoMLg
Little Fiddle: Shove the Pig's Foot a Little Further into the Fire
http://www.youtube.com/watch?v=vBIjR39WYfM
Hornpipe: Fisher's Hornpipe
http://www.youtube.com/watch?v=RDE97NgFrTg
Bonny Morn: Bonny Morn
http://www.youtube.com/watch?v=GO0ApLU9zAc
Hole in the Wall: Hole in the Wall (Henry Purcell)
http://www.youtube.com/watch?v=gp4Qx3ntzkQ
Nightingale:
"Nightingale" and "Birdsong" both have really generic names, and both names are often paired with "song" or "music," so they've been really difficult to find info on. "Fiddler's Dance," likewise; nearly every square dance sounds similar to it, so I'm sure they just took one at random, gave it a generic title, and put it in the game. There are thousands of such dances, and I don't want to listen to each and every one.
Edit: Found "Nightingale," as above, thanks to user Farsight! (post below)
The "Independence" and "Military" tunes are surprisingly difficult to get info on. I've heard some of them on TV shows, movies, in Revolutionary War museums, etc., but they're not often really performed on their own. I'm proud of having found the origin to Successful Campaign (Success to the Campaign). I'll keep looking.
Love Forever:
York Fusiliers: York Fusiliers
http://www.youtube.com/watch?v=fV8sH8SLS4g (10:35)
Washington Artillery March: Washington's Artillery March
http://www.youtube.com/watch?v=rRD6znkks7w
Road to Boston: Road to Boston
http://www.youtube.com/watch?v=TmuQgBf8ZIc
Independence Way:
The Reveille:
Successful Campaign: Success to the Campaign
http://www.youtube.com/watch?v=iWy4rHRozUA (3:26)
Morelli's Lesson:
To Arms:
And finally, as a bonus:
Sid Meier's Pirates! English theme: British Grenadiers
http://www.youtube.com/watch?v=U5_NJW-qmok