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All this is true; and another point is this: Archers are not in general big-ticket items.
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This is a possible explanation of why the hobbits may have been overlooked in the records of the big folk. Whether or not archery is considered to be of great importance depends on the culture. However, this makes it a little complicated.
The Dunadan were famous in the golden days of yore for their steelbows. To anticipate matters somewhat, the Gondorians were willing to rely heavily on the bow in their warfare in Ithilien, and certain areas of Gondor seemed to be famous for their bowmen. It is hard to make a comparison of the attitudes of the Arnorians regarding the bow since their society had sort of ceased to exist.
Whether hobbit bows would have been much use against armored enemies might be a matter for wild and unfounded speculation (particularly if the hobbits were only two feet tall

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Especially little archers, probably dressed in green.
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I think this is the key to the explanation. There were probably only a comparitive few hobbit archers present and they may have been of very limited use (if any at all). People there at the time may have forgotten that the hobbits were present.