is it ok to strim knee high grass in winter?

Strim the grass now, clean off what has been cut.
It will blanch but will recover. Best done now than later.

I agree, don't take a lawn mower to it now, just strim or use hand held hedge trimmers to cut it down to a couple of inches. Use a grass rake to collect the cuttings and it should be ok until the spring when it starts to grow again and you can cut it with a mower, don't be too eager to get it too flat with the first cut in Spring.

Yes, it will be ok to strim now, just make sure you remove the cut grass