That's a much more complex question than you would think. While the Unicode Consortium decides what emojis go where in the set, and describe what each one should basically look like, it's up to each OS vendor to draw their own version. Full list here:
https://unicode.org/emoji/charts/full-emoji-list.html
As an example from the list, here's face with glasses:
Since I'm on an Apple device, Browser (the one in use on your platform) and Appl will always look the same. But all of the others are different since they were created by an artist for that platform. In other words, Apple drew/created all of the emojis used in its set. As such, you could easily infer that Apple owns the copyright for every emoji character they created.
And it gets more complicated than that. Here's a list of every organization or individual who contributed the artwork.
https://www.unicode.org/charts/fonts.html
Most notable on that page is the big, fat notice:
I'm no lawyer, but it sure looks like, as with many other fonts, there are copyrights to consider.
You can contact Apple legal and ask for clarification, but with so many hands in the creation of emojis, that may not be enough.