Are there any missable events?

Yes. One of the characters dies in the game. If you don't complete that character's events before then you'll have missed them.

Specifically the character Eda dies. Like your other farming rivals she has rival events that are triggered by reaching a certain number friendship points and reputation points. These events can also only be triggered at certain times an places. You have until the end of Fall of the first year to complete these events as she dies the next day on Winter 1.

You can also apparently miss flower events of your chosen marriage candidate if you attempt a reverse ring exchange. Normally the marriage process requires that you give him or her a commitment ring before the last two flower events are unlocked, but you can instead have the candidate give you a ring instead. To do this you need to give the candidate a lot of gifts. I'm not sure why exactly but it's been reported that this can cause you to miss flower events if the gifts are good ones, since after the reverse exchange you'll be at a pretty high flower level.