The Cloak Dance is just what it says, basically a kicking dance for kids. Sword dancers or cavaliers would also wear Cloaks when they danced all the way back to the 1500s.
below parapharsed from F.C. Notts book entitled "Stage and Fancy Dancing" circa 1896:
Tempo: Mazurka, Mod.
There is also a cloak dance from Ireland as well, may be related to this American / English childrens dance. During the early 1900's the typical female dance costume in Ireland consisted of a hooded cloak or shawl over a white dress with a sash. Girls costumes were colorful (Green, Red, White Saffron etc.) with a little embroidery and the Boys costume were subdued to baisc colors. The clip on the right is of such.