First off, Siberia is an enormous region that ranges from way above the Arctic Circle to the Mongolian border...it really depends on where she'll be as to how extreme the cold is. Assuming she'll be in one of the larger cities like Novosibirsk or Krasnoyarsk, which are farther south, the weather there is a lot like the weather in the central plains states of Canada. Winter's down in the -30C range normally (daytime), but can be colder. A heck of a lot of cold-weather clothing is absolutely essential. Most definitely, she should bring a warm hat, warm boots, and warm gloves/mittens in addition to a very warm coat.

In my trips to the region in winter, I've worn Sorel boots (super warm), fashionably paired with my long shearling coat, a huge wool scarf, and a fur hat. Russian women wouldn't be caught dead in Sorels, or any boots like them, but there's a lot of difference between me and a Russian woman. I pick warmth over style in such situations.