Let's look at it by changing the verb and the context.
Don't put your boots away yet because you will wash them.
Don't put your boots away yet because you will be washing them.
This makes it a bit more clearer I feel, as the first sentence doesn't really make any sense.
Using the "be" form suggests a definite future event to come.
With regards to "need", I feel the "you will need them" form, implies, not a single future event, but a more general sense of needing them for the future. To me it feels like it represents a presumption (i.e. with no definite future event in mind), but one that is generally accepted as being reliable, at least in the mind of the person who says it; it's a "goes without saying" thing.
You'll need them for the winter.
Sounds a lot more natural than:
You'll be needing them for the winter.