Thermal layers? Like the thin under layer you can buy at outdoor/sporting goods stores. It's lightweight, so won't be a problem for carrying around later (but she may want it anyway for Beijing in February!).

One of those fluffy tube scarves - can be worn around the neck, or pulled over the head and down the shoulders almost like a removeable turtleneck/hood all-in-one.

Wool socks. There are really cozy ones that double as compression socks sold in many pharmacies, in airports, on BC ferries.