I still agree with winter burn.  As the weather warms, quite often the affected plant parts show the damage even more.  As your tree is budding, it seems to have been surface damage.  You can trim out the dead, brown material.  It may look a bit strange to begin with but the shrub will fill out.  Do not take off the branch but only the dead needles.  Even though you wrapped the juniper, it is possible it went into winter lacking enough moisture.  Make sure to consistently water it.  Then water it until the ground freezes next fall.  I love this shrub.  It has beautiful color and form.