> presents agents as always ultimately thwarted by forces beyond human control

The implication of "rain on your wedding day" is that your wedding day is something you plan out extensively, trying to create some perfect event. And yet it can still be thwarted by weather. Obviously it takes some interpretation since it's a situation compressed into a 1-line song lyric but yes it can (and should, given that the song is called "ironic") be read as an example of cosmic irony.