We'll get to where ghost has to open the door an have all the enemies dead but its not progressing us to the next part.
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As of patch 1.1.2, this has been a glitch with the Winter's Run strike. It is not intentional, so a fix will be coming eventually. The bug only triggers when your fireteam (or just yourself, if you're soloing it) is camping up on the rock outcropping above the battlefield. You'll need to have someone stay by the door to move onto the next wave. Best of luck guardian!
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Just have two people snipe on the rocks and one guy go activate the door and just let him sit behind the rocks beside the door