Sometimes.
If it's a pure WW, then yes. Sometimes a hybrid with strong WW genes will start to change, but it won't be perfect as the hybridization effects the colour change. My little Todd isn't pure but he has very strong WW characteristics - he and his brother changed colour and went almost completely white but for the dorsal stripe. His only flaw was an odd white spot on his back when he changed back.
In captivity, they don't necessarily change colour in winter. It's all to do with how much daylight they experience, as short hours of light would cause the hamster to react as though to winter photo periods.
For example, Toddy was changing colour in June, because his tank in the shop was in a dim corner, and the lights were only on for opening times from 9 - 5:30.