sled, sleigh, snowshoes
橇 centers on a vehicle that slides over snow or ice: a sled or sleigh. Snowshoes are a related walking device for snow, sharing the idea of moving over snow without sinking.
橇 combines 木 (wood) with 毳, which likely contributes the sound and relates to fur or hair, suggesting a wooden object associated with fur or soft material—possibly a sled with fur coverings or used on snow. The exact historical development is uncertain.
The left side 木 is wood, and the right side 毳 looks like a hairy or furry shape. Imagine a wooden sled covered with fur to keep you warm as you slide over the snow.
For キョウ, picture a sled racing through Kyoto in a snowy festival: Kyoto -> キョウ, and the wooden sled glides over the snow.