This cushion is made of down.
This futon uses a lot of down.
その鳥の羽毛はとても美しい。
The bird's plumage is very beautiful.
鳥の羽毛が抜けて床に落ちていた。
The bird's feathers had fallen out and were lying on the floor.
The craftsman gathered down to make the futon.
羽毛 is the standard Japanese word for down/feathers, while ダウン is a loanword typically used for down as a product material (e.g. down jackets, down comforters).
羽毛 is the more specific, often formal term for down or feathers (as in bedding), while 毛 can loosely describe a bird's soft covering too.
羽毛 is the standard, concrete word for feathers or down, whereas 羽衣 is a figurative, literary expression for plumage.
羽毛 (feathers/down from birds) and 羊毛 (wool from sheep) look similar since both end in 毛, but they come from completely different animals and materials.
Composed of 羽 (う, 'feather') and 毛 (もう, 'hair/fur'). The reading うもう is the standard on'yomi compound reading.