Rosh HaShanah has two opposite aspects, one of judgment, and one of Yom Tov. We spend the day(s) in prayer and literally plead for our lives. Yet we eat festive meals and drink wine for Kiddush.
Is it acceptable, or even encouraged to drink festively on Rosh HaShanah?
The Shulchan Aruch Harav writes (597:1) (based on Rishonim and Tur/Shulchan Aruch):
ומצוה לאכול ולשתות ולשמוח בראש השנה כמ"ש בסי' תקפ"א אמנם לא יאכלו כל שבעם למען לא יקילו ראשם ותהיה יראת ה' על פניהם
My translation:
It is a mitzvah to eat and drink and rejoice on Rosh Hashana, as is explained in Siman 581. However one should not eat to full satisfaction so as not to come to lightheadness, and the fear of Hashem should be on their faces.
Similarly in 583:4 he writes:
ונוהגין לאכול בשר שמן ולשתות דבש וכל מיני מתיקה כדי שתהא השנה הזאת מתוקה ושמינה וכן כתוב בעזרא אכלו משמנים ושתו ממתקים
We customarily eat fatty meat and drink honey and all types of delicacies in order that the coming year should be sweet and fatty, as is written in Ezra: "Eat of the fat and drink of the sweet [.. for this day is holy to Hashem]".
Although the Beit Yosef (OC 597) quotes the Kol Bo that some have the custom of fasting on Rosh HaShanah, most rishonim hold that fasting is inappropriate and that one should eat, drink, and rejoice on Rosh HaShanah, and the Shulchan Aruch paskens accordingly (with the caveat that the rejoicing should be tempered by reverence for the day). This accords with the pasuk quoted in Michoel's answer (Nechemyah, 8:10).
Because of those opinions that fasting is appropriate, the Shulchan Aruch writes (based on the Agur) that if someone fasts once, it is considered that he has accepted that practice and he must subsequently fast on every Rosh HaShanah. The Rema writes that he should get the custom annulled instead. Notably, R' Yosef Karo in Maggid Meisharim praises the custom of fasting on the first day of Rosh HaShanah (Siman 40). I have heard that this encouragement to fast was relegated to the Maggid Meisharim because R' Karo felt that fasting is only an appropriate approach for rare individuals.
