Just a note that forest/wood in OSM doesn't mean a literal wood, but any sufficiently densely wooded area where you wouldn't want to map each tree. That's how it's done in practice, at the very least. And if it's thick enough, then it can cross footways and such. So it's fine to have wood areas here. And rest as grass with individual trees or may be scrub or whatever it is. An open-sky park versus a wooded park are quite a big difference if you consider, for example, comfortable temperature you can still stay there.