Please, be very careful with "usually" (especially "usually wooded").  It's a very slippery slope (semantically); it's very easy to make assumptions and slip / fall down.

The wider practice that seems to be working is to "break apart" a dual-tagged (or assumed to be "both" wooded BECAUSE it is a "natural state" thing — around here — single-tagged thing) to TWO polygons.  One for the, say, leisure=nature_reserve, one for the natural=wood which may sort of and sort of not be landcover in the area.  You do need two polygons because you can't assume that "one means the other."  (Around here).  It doesn't.  That assumption must die, or we'll continue to have misunderstandings like this.

So, really, there are THREE things here that might be tagged separately:  the leisure=nature_reserve (which draws a boundary) the landcover (maybe wooded here, swampy there, grassland in patches here and there...) AND maybe there is a "front of park" area which could be subsetted with a small polygon tagged leisure=park.

Is everybody happy now?!  We can do this!