I think one could say either 결혼식 때 입던 옷 or 결혼식 때 입은 옷, depending on the circumstances.
In regard to clothes, we wear them, take them off, and then wear them again later, so 어제 입던 옷 (the clothes I wore yesterday) seems more appropriate than 어제 입은 옷 since 입던 would imply a interruption in wearing the clothes, in other words, a change of clothes. Then, what would 어제 입은 옷 imply? It might imply one wore the clothes yesterday, but no longer has the clothes to wear again today.
In regard to a wedding gown, many women in the West wear them just once, but still keep them for sentimental reasons, and some mothers may even allow their daughters to wear their old wedding gowns when they get married, so, in the West, I think a wedding gown could be treated like any other piece of clothing by saying 결혼식 때 입던 옷.
In Korea, however, Koreans normally do not buy their wedding gowns, but rent them, so in Korea, it might be more appropriate to say 결혼식 때 입은 옷 since Koreans would no longer have the wedding gowns to wear again.
Koreans also seem to use 입던 옷 to refer to clothes they no longer wear because they are either out of style or because they no longer fit. Therefore, 입던 옷 seems to refer not only to clothes that we wear on a regular basis, but also to clothes we no longer wear but still have. The common denominator seems to be that one still has the clothes, whether they are worn or not.
The above is just a theory. I do not know for sure if 입은 옷 really implies one no longer has the clothes.