One of my biggest frustrations with OSM is adding non-forest/wood areas to an otherwise completely tree-covered area of land.

I'd like to know if there's any way to invert the selection of say, grassland, to have everything around it be wood. Or conversely, if it's possible to place grassland on a wooded area that would cut it out, instead of just overlapping it?

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    Does this answer your question? Gives suggestions for all 3 editors (Potlatch, Id, JOSM). Not tried this myself so I'm not sure whether it makes a hole in the outer polygon (which I think is what you're trying to do), or simply overlays the inner polygon. – Steven Kay Jan 3 '16 at 21:37
  • @StevenKay Yes, that'll do it. Thanks very much. If you pull the content over into your own answer (for posterity), I'll be happy to accept it. – David Metcalfe Jan 3 '16 at 21:43

This page on OSM help covers this, and gives suggestions in Potlatch, iD and JOSM.

Summarising off-site link: the mapping editors allow conversions of groups of selected polygons to convert them to relation multipolygons, and have a merge tool to allow this in each of their editors.

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