There is currently no agreed way in OSM to map a highway as an a closed area (a polygon) rather than a linear way (a polyline).
polyline). Indeed, mapping solely as an area would break a lot of rendering and routing software which expects highways to be linear.
The subject is [under discussion by some people][1]. However, with the best will in the world, the people discussing it are not developers and so it is not necessarily the case that whatever scheme they devise will ever be adopted by any rendering or routing tools.
Some people, myself included, are of the firm opinion that to do this "properly" would require API-level changes rather than just messily grafting on new metadata within the existing spec.
spec. It will also require serious thought as to how the option is presented in editing software while maintaining an understandable and coherent UI.
For now, I would suggest that you map using ways, and if you still have some spare time, find some more stuff to map!
[1]: http://gis.638310.n2.nabble.com/Feature-Proposal-RFC-area-highway-td6351114.html