Is the park open during the winter

You should check the snow level ... it's supposed to be opened but it depends if the roads are able to be used !

Yes, and it can very beautiful with the Sequoia trees against snow. But be warned that because of the high elevation, carrying chains is required in the park, and may become necessary to use.

It is but with those windy roads I'd think twice

Always take chains because after a higher level you must be cautious about the frozen roads, it's opened but be prepared for higher levels of snow and ice. Snow chains or cables are a must.