The highest High Plains campsite is above Whiterock Falls, but it could be a bit exposed, even if you go down in the gully in the lee of the slope. Some parts of the road to Big River are flat enough for camping but could be lumpy. Just before Big River on the High Plains side there's a good clearing.
The next reasonable campsite is at Big River Saddle, a short way from the Quartz Ridge turnoff. Going up Quartz Ridge there are a number of flat areas, with snow melted for water. There's a campsite on the treeline, maybe 1700 metres. The picture below is by Mark Oates from his winter AAWT article in BWA October 2019.
Above that it's exposed, nice if the wind is not blowing but not much fun in a blizzard. At a pinch you could drop off the east side and make a bench, but it's steep. You may get shelter in a gully that I believe is just north of Quartz Knob. Although the gully is reasonably flat and in the lee of the hill, if the wind comes from the south-west you will be hang gliding.