My local trails are the South Downs which is largely slick chalk or claggy clay, both a nightmare during the winter months (except when frozen…fantastic fun!).
However, in any geographical area there are always trails which stand up to rain better than others. We tend to head for the woods during the winter. Although it’s muddy and the autumn leaves make the singletrack difficult to follow, it’s also sheltered from the wind/rain, and it makes the mud fun to ride in by adding that extra challenge of the trees / logs / roots etc (better than wet chalk any day!).
It also teaches you to relax, control pedal power more effectively, and definately makes you a much better rider come the spring.
No riding during the winter months just isn’t an option for me.