Paul
I'm pretty sure you didn't mean mutually exclusive.
As a math geek I'd like to expand:
Winter is neither necessary nor sufficient for winter conditions.
Winter conditions are neither necessary nor sufficient for Winter.
However, the two are highly correlated. I'll finish with a Venn Diagram.
Here is a Venn Diagram of Winter and Winter Conditions. Note the large overlap, but also the nonempty complement of the intersection.
And here, for instructional purposes, are two mutually exclusive sets.