帽

Left radical 巾 - a piece of cloth hanging from a horizontal rod, the picture of a kerchief. Marks 帽 as a textile object worn on the body. Same radical anchors the cloth-family: 布 (fabric), 帘 (curtain), 帆 (sail), 带 (belt), 席 (mat). Anything woven sits in this family.

Right phonetic 冒 supplies the full sound mào with no drift, and a strong layer of meaning: 冒 itself originally pictured a hat over an eye, the picture of headwear. So 帽 is essentially 'hat' written twice - first the cloth radical, then the older hat-graph 冒 - to disambiguate after 冒 took on extended senses (risk, brave).