Don't know if it's changed, but the main car park at Swinley was closed anyway on Wednesday. In my 2 wheel drive car I attempted various parking places nearby but anything off the road was just resulting in me getting stuck. Even the car park at the water park was a nightmare.
What's the road like over Tunnel Hill? That's normally my route to work, but I've avoided it over the last few days. I've skidded down round those bends before and it's not nice (it's a dangerous enough road as it is without ice on top). If you can get to the car park by the canal that would be sufficient though.
Think of trying Surrey Hills today. They were great before Christmas in the snow and surprisingly easy to ride in the snow. I guess could be too much now, and I suspect it's impossible to drive there.