I rode Ringwood yesterday morning when it was below freezing on a Fatbike. It was quite ride-able. There are bare patches in some spots and then there are other areas with several inches of snow still to melt...depending on exposure. This goes for fire-roads and single-track.
The conditions over the next several days will likely change dramatically from what I experienced yesterday though. It is warming and raining. So, all that snow will be melting and creating mud.
I think you'd be messing up the single-track if you rode it, but there are plenty of fire-roads you could ride.
Here's a few pics of the mix of conditions from yesterday.