While the Callahagn Valley (location of WOP) is very beautiful and the snow is more reliable up there, there is snowshoeing right in Whistler Village.
The snow tends to melt in the village pretty fast, so conditions can be iffy, but the Lost Lake area is very pretty and easy walking distance from the centre of the village.
If you are keen to get up to the Callahagn, then your options are pretty limited. They used to run a bus, but I don't think they got enough business to be viable. You can get a taxi or rent a car from the Avis outlet in town. I know Sigge's runs a bus, but that comes up from Vancouver. You might also contact the ski lodge at Callahagn Ski Country and see if they provide any transport from the village.