I’ve just experienced this first hand. Contrary to the reports, some areas, particularly Folkestone, have received more than 15cm of snow. I stood in it and it was nearer 20cm and drifting.
I was supposed to have gone to Dover today and on to the Netherlands for work. Normally it takes me about 1 hour 40 minutes to get to Dover. After an hour stuck on the M20 going nowhere at the Channel Tunnel exit, I managed to get off the motorway and turned back. My round trip took me six and a quarter hours.
I can also recommend avoiding the B2063 Hospital Hill in Folkestone when it is like this. It is, um, interesting to descend when covered in thick snow and ice. The row of damaged and dented cars abandoned on the side of the road does not give confidence.