This looks like a fungal blight.  You will want to prune off the dead twigs going about 2 inches into healthy wood.  Burn or bury these twigs, or put them into the trash.  You want to choose a dry day for this when the plant foliage is completely dry and humidity is low.  Sterilize the pruners with rubbing alcohol between cuts.  Make sure to water only the roots of these trees- avoid wetting the foliage or brushing up against the foliage when they are wet. There are some fungicides that are labeled for twig blight on junipers, and these should be applied in the early spring.  Read more about juniper blight here: http://plantclinic.cornell.edu/factsheets/junipertipblight.pdf

Thank you for contacting Ask Extension.
Ruth