The original is (in spite of comments from other threads on this topic) truly the Spring Dance by Edvard Grieg, Lyric Pieces Op. 47 No. 6. This was originally composed by Grieg as a piece for solo piano. For this commercial, it was orchestrated. I haven't checked into whether or not Grieg made an orchestral version, but if he did, I doubt very much whether what you hear on the commercial is Grieg's orchestration. The original piece is in the key of G, the commericial's is in the key of F. Also, the musical form in the commercial's version has been compacted, and there are a number of melodic alterations. This is understandable, as the music has to fit a 30-second spot.
So I'd say a film/tv composer took some liberties and created a very effective accompaniment for this commercial. But the original piece on which it's based is definitely the Grieg. (I'm a pianist, and downloaded the score and played it myself.) I wonder if the orchestrator finished the piece. It's only 74 bars long. Would make a nice MP3! It would also have been nice to include it on the audio DVD that came with the car. (Yes, I bought the car! But not just because of the commercial music.} :-)