We have been snowed in at much lower altitudes (at the Charcoal Kilns already) in September or October, so... The trail is often covered in snow until June, and there can be knee-deep snow well into the middle of the year.
In winter you would surely need ice axes and crampons, and there can be ferocious storms that make hiking impossible. I would surely not try it in the middle of winter - but I am no extreme mountaineer. If you are one and well equipped you just have to be lucky with the weather.
Here is an interesting read about hiking there:
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