Here's a newspaper clipping from the North Mail & Newcastle Daily Chronicle, which is dated April 3, 1936.
We were able to get some more info from Walt Disney Archivist Rebecca Cline who explained more about the clipping:
It was put in to advertise a charity matinee being held at a theatre in Whitley Bay, Tyne, England.
The children's charity matinee The Wedding of Mickey Mouse, was an event that toured the territories of our British film licensees throughout 1936. This particular charity matinee and stage show was held in the seaside resort town of Whitley Bay. We also have clippings describing the same event happening in other theaters in London, Sydney and New Zealand.
So...it would appear that this proposal, while all so heartwarming, was actually performed several times over for audiences around the world.
Wow. As it turns out, Mickey and Minnie costumes from this era varied quite a bit.
Despite having several public weddings, it would appear as though the ceremonies didn't really count for the Disney couple:
From Archivist Rebecca Cline: "The company's position on Mickey and Minnie as a couple is that 'Minnie is Mickey's leading lady and best girl' and that although as actors they occasionally appear on film as a married couple, they are not married in real life."