Seasonal harvesting of trees would open up a lot of other options for the game, because its more complex than the herbs we have in the game right now. Right now, the herbs grow to maturity, they have a single product, and you collect the ripened product.
But for things like fruit trees, berry trees, and nut trees, you have several stages where you can harvest a different product. The tree will first grow flowers, and then the flowers will later develop into the ripened fruit, berry or nut. Often the flowers are just as usable as the ripened product, and can be made into things like teas, syrups, and liquors. Besides which, the flowers would make the game prettier and would be a sign of spring.
A long time ago, when I did the herb tile sprites, one of my main interests was bog-myrtle. Its not a tree but grows as a bush; and that goes through stages of development through the year from flowers, to nuts, to fruit, and all of these are usable. So, ideally, you'd want to be able to harvest the flowers in one season, the nuts in another, and the ripe fruits in another. And then you have something similar with roses, too, where you can harvest the flowers for the rose petals to use those in cooking, or wait until the rosehip matures and use the fruit.
Anyway, something like hazelnut is also appealing, even if it will be a less common tree in the game; because something that makes the game enjoyable over a long term is going on long trips hunting down rarer items, either for your own use as a player or for trade purposes. I could collect a bunch of hazelnuts down south and venture up north to trade with villagers who wouldn't normally have access to them.