A late November-December pilgrimage?

Not sure what you mean by 'practical', but there have been various other threads on walking in the winter months. If you're worried about the weather, it will be colder of course, and there may be snow on the various mountain ranges. If so, take a lower-level route around them; there is always a road of some sort. If it's blowing a blizzard then wait for it to subside; it's unlikely to last long. As I've said in another thread, IMO the bigger problem is the short daylight; make sure you know when it's going to get dark and allow plenty of time to reach your destination before then. 'Better safe than sorry' but then again 'where there's a will, there's a way'.