Just to add briefly, one other battle that gets lost in the mix was the Battle of Moore's Creek Bridge (Febuary 27, 1776 at Willmington, North Carolina).

This pitted the local rebel faction against the Highlanders of Cross Creek & other loyalists. Some of the Highlanders were carrying traditional weapons, including broadswords. I've also read some accounts (including the NPS) that have some of the Highlanders wearing tartan (kilts etc) & charging into battle to the sound of the bagpipes.

Interesting points:

Those Highlanders who pledged service to the Crown, the British government promised 200 acres of land, cancellation of land fees, and tax exemption for 20 years.

Major Donald McLeod (one of the leaders of the Highlanders) gave the battle cry "King George and Broadswords!" to rally his men when stalled at the bridge (they subsequently lost the battle). McLeod went on to help form the 84th RoF Royal Highland Emigrants.

Flora MacDonald (yes, that Flora MacDonald, of '45 fame) helped raise the Highlanders of Cross Creek for service. Her husband was one of the officers involved.

The Moore's Creek NPS site
look for a small photo of the diorama that shows Highlanders in kilts & bonnets...

Moores Creek National Battlefield: An Administrative History - By Michael A. Capps and Steven A. Davis
Includes an artist rendering of the failed assault upon the bridge, note some of the Highlanders are depicted in full Highland dress...

Additional links:
http://www.myrevolutionarywar.com/battles/760227.htm

http://statelibrary.ncdcr.gov/nc/ncsites/moores.htm

http://www.patriotresource.com/battles/moores.html