Is it appropriate to ask Active Duty soldiers to dress in ASU's for a wedding?

Congratulations on your upcoming nuptials! Several things come into play here. First of all, is it going to be a military wedding, or a civilian service? If Military, it is a given that all service members would wear the appropriate level of dress uniform and the invitation should state the appropriate attire for civilians. If it is a civilian service, the invitations should simply state the level of formality: casual, semi-formal (suit)l, formal (black tie) (normally only for events after 1700).
One other thing, if wearing the ASU and the ceremony is after 1700hrs, headgear is optional, and the black bow tie should be worn in lieu of the fore-in-hand tie (the difference between the ASU as semi-formal or formal).
All that being said, it is indeed your wedding (well.. actually HER wedding, but you'll learn that as you go! LOL!) and you are certainly free to do as you wish as far as the invitations go.

Congratulations/commiseration to you. Welcome to the club.

I think the operative word that you used was request, and therefore I think you answered your own question. It is entirely appropriate for you to make a request. As long as you understand that a request leaves the option for something else.

PFC Cedric Powell, first congratulations! And if the guests are active duty military, I wouldn't see any problem asking them to wear their ASUs. It is an issued uniform item, so everyone should have it in serviceable condition. Plus it is the civilian equivalent of formal wear if memory serves me correctly. I've been at a wedding this summer where the groom and several members of the wedding party were in ASUs and it looked real sharp. I think the only thing you might want to specify is if you would like to guests to be in neck tie or bow tie. I believe that part may depend upon the time of the ceremony. There is probably something in AR 670-1 that would provide better guidance, but it is your wedding and I do believe it is appropriate to ask.