My families minhag is to wear a kittel just on Yom Kippur (so I do). But in shul I see a number of folk with the minhag to wear it also on Rosh Hashanah.
I know it is related to Yom Hadin, and whatnot for wearing it in the first place, but why the difference in minhagim between the two sets of days?
Shulchan Aruch (Orach Chaim 610:4) mentions it only for Yom Kippur, as part of the minhag to wear white so as to resemble the angels. That reason indeed only applies on Yom Kippur, when we also are like the angels in not eating and drinking, standing during much of the services, saying Baruch Shem out loud, etc.
Those who wear it on Rosh Hashanah too do so for the other reason mentioned there, that it reminds a person of the day of death (since a kittel is used, in most customs, as part of a man's shrouds) and therefore induces a feeling of humility and brokenheartedness.
Sorry for the huge quote, but I felt that it was written really well:
There are two reasons given why a kittel is worn:
1) The kittel, being a plain white garment, symbolizes purity from sin.
2) A person is buried wearing a kittel. Therefore, when a person wears a kittel he feels humble and remorseful for his sins, remembering the day of death.
According to reason #1, the kittel would only seem appropriate for Yom Kippur, when we are cleansed of our sins, but not for Rosh Hashana. Reason #2 is also not totally applicable to Rosh Hashana; although Rosh Hashana is a day of repentance, it is also a joyous holiday of solemn celebration and one should not display undue sadness.
In some communities the kittel is in fact worn on Rosh Hashana by all congregants. This custom is mentioned by Mateh Moshe and has its source in a midrash which describes how the Jewish people wear white on Rosh Hashana, confident that their sins will be forgiven. Perhaps the custom you mention, namely that the shaliach tzibbur, ba'al tokeah and ba'al korei wear a kittel is based on this midrash, due to their crucial role in the Rosh Hashana services.
