The wedding attire as seen in episode 15 is usually only worn by members of the royal family. There are different wedding attires worn by noble families. I won't go into detail because it could end up being very confusing.
So I will keep my focus on the particular wedding attire worn by Ha Yeon and Lee Yeong which is reserved by the royal bride and groom.
Ha Yeon is wearing the so-called hwarot, a traditional royal dress, worn during the wedding ceremony. It's a overcoat usually worn over many layers of clothes (jacket and skirt) underneath. The color scheme is blue and red – the colors of ying and yang. But the colors of the overcoat indicate the status of the bride. So a noble bride or a commoners bride will wear a wedding coat in different colors than a future queen like Ha Yeon. Also noble daughters and commoners weren't allowed or able to wear hwarot. They wore a wonsam instead (a overcoat).
The collar is adorned with the golden phoenix and the blue part is embroidered with birds and different ceremonial patterns. The black band over her shoulders is called wedding ribbon, with other attires it would be worn over the binyeo (hairpin) but the Crown Princess is wearing it over the shoulders. It's embroidered with golden clouds and phoenixes.
As a preparation for her status as a married woman Ha Yeon's hair is styled in jjeokjin meori. Meaning her hair goes up in a bun and is held by a binyeo (hairpin) in the back. The golden binyeo is also adorned with a phoenix. There are also many dwikkojis (hairpins) for the bun. On top of her head she is wearing the cheopji (hair ornament) only worn by brides.
Underneath the hwarot the bride is wearing special bride shoes, called flower shoes (ggossin). Those are covered in red and blue silk and embroidered with flowers.
The bridal look is completed with the daesu meori which is basically a type of wig OR a hat made of a wig, adorned with many different hairpins and ornaments. This type of headpiece is either worn for weddings or coronations. So get your seatbelts on, fellow Moonlighters, it's getting complicated.
The daesu meori is worn over Ha Yeon's hair and it's very heavy. In the back (what we can't see in the drama) the headpiece is adorned with a purple ribbon. The purple color indicates the status of getting married. The lower end of the wig is adorned with two phoenix binyeos (phoenix hairpins).
In the center of the headpiece we have a pearl ornament and on each side of it the dragon binyeo (dragon hairpin). Over it we can see the red and gold daenggi (hair ribbon) with many ornaments on it. Above we have two larger round ornaments and above that the butterfly ornament. On the top we have two phoenix dwikkojis (hairpins) and a keun binyeo (big hairpin). Also in the back 3 large binyeos. See pictures for names.
Now on to Lee Yeong. He is wearing a dark blue (inside is either red or purple) myeonbok, a traditional royal dress, adorned with the dragons on each shoulder (it's five-clawed), mountain on the back and trees on the sleeves. Underneath the overcoat he is wearing a white silk durumagi.
Over the myeonbok he is wearing a red sash, called daedae, and the another sash called pyesul with the mountain and fire motif embroidered on it. Those motifs are connected with ying and yang.
In the back he is wearing a sash, called husu, made of different types of fabrics. It's usually made of four different colors indicating the four directions/seasons. Over it he is wearing the belt and a pair of gorgeous pae (jade ornaments) attached to it.
In his hands he is holding kyu, a tessera made of white jade,
On his head he is wearing myeonrugwan, a type of head with many beads on it, only worn during weddings or coronations.