As the guy who first suggested Grieg, after listening to pldennison’s clip, I will suggest that BOTH are very commonly used in cartoons, BOTH are rendered with flutes, BOTH are used to set up peaceful morning scenes, and it is impossible for us to know which one the OP had in mind. In fact, the casual listener can be excused for conflating them into one melody in their memory, they are so similar in application as background music. If they OP wants to tell us which he had in mind, he should be sure to listen to clips of each first.
Something else which is curious is that they BOTH come from works with other heavily used and immediately recognized themes in them - Rossini’s overture yielding “The Lone Ranger”, and many commercials (“Have a lark, have a lark, have a lark today …” - WHY do I remember that) and Grieg providing the distinctive “In the Hall of the Mountain King”:
Apparently, Grieg wrote that ItHotMK should evoke images of “Cow manure and super nationalism”. So why do I get images of elephants sneaking around on tip-toe?