Why don't brides (always) cover their hair for their weddings? I understand that in some ultra-religious groups they do, but there seem to be many groups within Orthodoxy where they do not cover their hair either during the chuppah or during the reception. (A veil is worn, of course, but that hardly seems to be a full covering.) What is the reasoning behind leaving the hair uncovered during the wedding?
Per the Igros Moshe the bride does not have to cover her hair until the morning after the wedding. The reasoning is that so long that she retains a public presumption of virginity, she has no obligation to cover her hair.
The answer is that the Mishna (Ketubbot 2:1) says that a Betula goes to the Chuppah with her hair uncovered. So what is there to talk about?
Well, there's a responsum (#9) of Mahari HaLevi (the Taz's brother) where he rules that even an Arusa needs to cover her hair. This position seems difficult in light of the above Mishna (and indeed see Yechavveh Daat 5:67 that many, many opinions argue on it) but it was quoted by R Akiva Eiger (OC 75) and further cited by the Mishna Berura (ibid. sk 11), so it has gained a lot of standing (see, eg. Teshuvot veHanhagot 4:294 who requires a full hair covering after Kiddushin because of it). However, Mahari HaLevi was aware of that Mishna and if you read his responsum inside, you'll see he thinks that an Arusa needs to cover her hair for the long period of time that existed once upon a time between Eirusin and Nissuin, but at the Chuppah she can uncover much of her hair because that was the custom so it is not a violation of Dat Yehudit which is by definition dependent on custom. Accordingly, even according to Mahari HaLevi (and seemingly, thus, those who rule like him) a bride need only wear a partial (like a קלתה) hair covering (eg. a veil) for the biblical requirement. This is also the position of R Mordechai Willig (here minute ~30).
If you reject the opinion that the obligation starts at Eirusin, you need to draw a different line. One way to approach this is claim that only a Beulah (or, possibly, a women who is presumed to be a Beulah) needs to have her hair covered. Although being a Beulah seems like a reasonable place to draw the line (because an Arusa is still pretty much just as married as a Nesuah so it must be something else -- R Moshe Feinstein -- or because until the marriage is consummated she cannot become a Sotah (Bavli Sotah 24b) which is the source for hair covering -- R Yehuda Herzl Henkin -- or because all Beulot need to cover hair even without marriage -- eg. Chelkat Mechokeik EH 21:2), this gets tricky, because at Ashkenazi weddings, at least, Yichud happens before the party, at which point she could technically already be a Beulah. While we all know that's highly unlikely, Halacha does have a principle (Rambam Issurei Biah 19:3) that any Nesuah is presumed to be a Beulah even if they never consummated the marriage (" שכל נשואה בחזקת בעולה היא אף ע"פ שנמצאת בתולה"). Furthermore the Yerushalmi (Ketubbot 2:1, at least as understood by Penei Moshe and Korban haEeida that "Lo Shkhicha" there is only referring to Mukkat Eitz) says that a Betulah who is a widow from Nissuin does not go to her wedding with her hair uncovered, implying Nissuin alone is sufficient. Indeed Rav Ovadia Yosef (Yechavveh Daat 5:67) rules that a woman must cover her hair immediately after Yichud once she is a Nesuah.
However, R Henkin argues (Benei Vanim 3:23) that even if one rejects the above reasons for the biblical obligation not coming into effect until the marriage is consummated, one would have to agree that there is no biblical obligation in the wedding hall because the biblical obligation is only in publicly accessible place (like the marketplace היוצא לשוק or חצר שהרבים בוקעים בו) not to a private gathering, even if it's big. Furthermore, R Henkin argues that the Rosh (Ketubbot 2:3) implies that the original permission of leaving the hair uncovered lasted the entire first day, not just at the Chuppah itself.
He thus explains, not unlike the Mahari HaLevi, that since we are only dealing with Dat Yehudit, in a location where the custom is to leave the bride's hair uncovered that is acceptable. (Were she to leave the hall, though, she may need to cover up, at least partially.)
A veil is worn, of course, but that hardly seems to be a full covering.
I learned that due to the large argument about when the bride first must cover her hair, it is sufficient at the wedding to have a partial covering which satisfies the Biblical requirement (dat moshe) but not the rabbinic requirement (dat yehudit). [See the Talmud Ketubot 72b where a קלתה is described as fulfilling the Biblical requirement but not the rabbinic one.]