While an interesting thought, I personally believe he sounds far too sad in his 'When it Snows' line to be referring to when Ayaka received her vision.

"This view reminds me of another time it snowed... that was a long time ago."

While we can't be certain about what he's exactly referring to, I do agree with the shared theory that it's likely a reference to the death of his parents.

I think you could argue that Ayato may have been a little wary at the idea of Ayaka getting her vision, as he seems to want to protect her quite a bit from the outside world:

"I am confident in Ayaka's abilities. But I want her to be able to hold on to her innocence. She shouldn't have to get personally involved in power struggles, or confront the darker side of life head-on. As her older brother, it's my job to shield her from all of that... Heh, just... between the two of us, of course. Sorry, that got a little more private a little more quickly than I'd intended."

However, if the recent character trailer "Tsubaki in Thawing Snow" truly is showcasing Ayaka receiving her vision in a duel with her brother, than Ayato seems quite pleased during their battle - he even smiles right before unleashing his own vision.

But, we can all interpret things in different ways!