There are no seasons in the game. There are only days of the month in the game. Every 25th day is Christmas, and every last day of the month is Halloween.
Viewing post in Daily Lives of My Countryside comments
Two crops regrow, cucumber and corn. At least cucumber indicate they regrow on their own in its description for them anyway. Just like corn does.
Two do not, turnip and potato, IIRC.
Seeing as how we are in this for the long game anyway seeing as how it takes the time it does to navigate through all of the NPC's events, I figure why not just plant all of the crops that regrow on their own to begin with seeing as how there are no recipes that require turnips or potatoes or no NPC's request them either.
Even if they take longer to initially mature, if they continue to fruit forever, you're better off in the long run going this route to begin with, I figure.