It's both. Yes the air is saturated and yes it's because the air is cold. If you take a cubic meter of air at sea level that has half the water vapor in it that it could hold, the relative humidity is said to be 50 percent. If you raise that cube of air it's temperature will normally drop 2 degrees per 1000 feet. As the temperature drops, the total amount of water the air can hold decreases and so the relative humidity increases. At some altitude the air cools to the point it can no longer hold any more water and it is said to be saturated. Now the air's RH is 100 percent.
Start at page 15 of the download, page 37 of the book.
http://www.faa.gov/documentLibrary/m...Chap%204-6.pdf