According to Rashi it's the high priest, which would seem to make sense to me if you look at verses 3 and 10 onward of Chapter 44, which first deals with Leviim and then with kohanim. It goes into the particular ways they dress also, almost like royalty has specific garb, and then how they judge in line 24. And in 43 line 19 the priests are mentioned in the name of Zadok, the high priest in the time of Solomon, which is another clue. Also zadok may hint at rightousness being restored among the priests, my guess.
And in 45:8 it mentions princes during a discussion of the priests, in a reference that the land will not be theirs, which is something that had already been discussed in this section of Ezekiel.
Rashi says, however, in the name of Rabbi Menachem (?) in a comment on line 17 that prince there and everywhere else might actually mean king. I don't see conflict here. Anyone can make an offering at the Temple. It's just the priests who officiate it. That would actually make sense based on 46:2.
From a more modern perspective, this whole thing makes complete sense if it's the king. Ezekiel is supposedly a priest. He's reflecting priestly concerns that the kingship still support the structure of the Temple Cult in an open way, even to the point of appearing before the people as having made an offering, coming out the main entrance, so to speak, which would encourage the people to support the Temple as well. It also reminds the people that the priests gave up property holdings so that they could do the God stuff. So I think it's more than likely this is referring to the king.
Dauer