Is it permitted for a retiree to wear their ASU for their wedding day?

That is the perfect example of when wearing a uniform is more than just permitted it is admirable. (just get your wife's buyin first, it will set you up for later matrimonial success)

Here is a link to the current AR 670-1.
http://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN6173_AR670-1_Web_FINAL.pdf
Chapter 21
Wear of the Army Uniform by Reserve, Retired, Separated, and Civilian Personnel
21–1. Occasions of ceremony
a. As used in this regulation, the phrase “occasions of ceremony” means occasions essentially of a military character,
at which the uniform is more appropriate than civilian clothing. These functions include, but are not limited to, military
balls, military parades, weddings, military funerals, memorial services, meetings, conferences, or similar functions of associations
formed for military purposes, of which the membership is composed largely or entirely of current or honorably
discharged veterans of the Armed Forces of the United States. Authority to wear the uniform includes wear while traveling
to and from the ceremony or function, provided the travel in uniform can be completed on the day of the ceremony or
function and must follow guidance included in paragraph 3–7c.
b. All persons wearing the Army uniform will wear awards, decorations, and insignia in the same manner as prescribed
in this regulation for active duty Soldiers. For civilian attire, individuals may wear only those awards, decorations, or
insignia authorized by this regulation for wear on civilian clothing, in the same manner and approximate location as the
equivalent military uniform.

Yes In the same proper manner you would have worn it while on Duty. The rules are specified in army regulation AR 670-1. It also outlines when and how a civilian is entitled to wear the uniform.