1. Harav Ephraim Zalman Margalios zt”l, in his Sefer Mateh Ephraim (602:5), writes that the custom is to refrain from marrying during the Aseres Yimei Teshuvah (Ten Days of Repentance, beginning with Rosh Hashana and ending with Yom Kippur). The opinion of the Mateh Ephraim was also cited by the Kitzur Shulchan Aruch (130:4).
2. There are many reasons given for this stringent custom. The most obvious reason is that the Aseres Yimei Teshuvah are very serious days, days that are meant for prayer and repentance. Because weddings can cause frivolity and drunkenness it is not appropriate to have weddings during that time of the year. (Minhag Yisroel Torah on Nisuin)
3. Harav Dovid Tzvi Hoffman zt”l, however, in his Sefer Melamed Lehoil (E.H.1), writes a fascinating responsa regarding this subject. He writes, “I have seen in the Sefer Mateh Ephraim that one should not marry during the Aseres Yimei Teshuva. This was also codified by the Kitzur Shulchan Aruch. This halacha can also be found in the siddur of Harav Yaakov Emden zt”l. However, I have searched and not found an earlier source for such a stringent custom. It also appears to me that this stringent custom has not been widely accepted. This does not seem to be the view of the gedolei hador (leaders of the generation). Indeed, my wedding took place on the sixth of Tishrei in the year 5633. My father in law, the saintly Harav Yonah Rozenbaum zt”l, was slightly unsure as to whether my wedding may take place during the Aseres Yimei Teshuva. He asked Harav Zeligman Bar Bomberger zt”l who ruled in the affirmative and added that fulfilling the mitzvah of getting married and having children will help the young couple gain atonement on Yom Kippur. I, therefore, married during the Aseres Yimei Teshuva and neither my teachers nor my friends raised any objections. Therefore, it seems clear to me that one who has not yet fulfilled the obligation of having children should not avoid getting married during the Aseres Yimei Teshuva. However, one who already has children, and therefore marriage is not as great of an obligation, should delay the wedding until after Yom Kippur. After writing this letter it was brought to my attention that the Sefer Darchei Noam cites that Harav Azriel Hildsheimer zt”l permitted weddings to take place during the Aseres Yimei Teshuva.”
4. The Tzitz Eliezer (7:49:11) cites the opinion of Harav Dovid Hoffman zt”l and states, “It appears to me that the common custom, especially among Ashkenazic Jews, is to refrain from marrying during the Aseres Yimei Teshuva. However, when necessary one may rule leniently.”
5. The Chazon Ish (Maaseh Ish vol. 2 page 211), Harav Yosef Shalom Elyashiv zt”l (Yivakshu Mipihu page 393), and Harav Ovadia Yosef zt”l (Yechava Daas 1:48) rule that one may get married during the Aseres Yimei Teshuva.
6. Harav Ovadia Yosef zt”l continues that one should even urge others to marry as soon as possible, even if that means that the wedding will take place during the Aseres Yimei Teshuva. This applies especially if the chosson has already reached the age of twenty.
7. The period of time between Yom Kippur and Succos is an auspicious time for weddings. (haeirusin V’Hanisuin page 437)