You will see it both ways. Including the definite article "the" or not slightly changes the meaning. If we say "the early spring of 2009", then the intended meaning is that in 2009 the spring was early. However, if we say "in early spring of 2009", then the implication is a time toward the beginning of the season.

"In the early spring of 2009." The other way is just clumsy.

"In the early spring of 2009"...is right.