How can I get rid of a lot of branches and twigs now that we're in the dead of winter?

A recent storm knocked down most of a tree near the back of our house and we had to chop as much of it as we could...unfortunately we have a lot of twigs and bigger branches outside.

We have a fireplace but are from the west coast and don't know how to begin to know how and where to store it....little help please?!
 
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