Index: src/applications/project/controller/PhabricatorProjectBoardViewController.php
===================================================================
--- src/applications/project/controller/PhabricatorProjectBoardViewController.php
+++ src/applications/project/controller/PhabricatorProjectBoardViewController.php
@@ -254,6 +254,13 @@
         continue;
       }
 
+      if (!$this->showHidden) {
+        if ($proxy && $proxy->isArchived()) {
+          // Hide archived milestone / subproject columns by default.
+          continue;
+        }
+      }
+
       $task_phids = $layout_engine->getColumnObjectPHIDs(
         $board_phid,
         $column->getPHID());
@@ -307,7 +314,8 @@
         $panel->addClass($display_class);
       }
 
-      if ($column->isHidden()) {
+      if ($column->isHidden() ||
+          ($column->getProxy() && $column->getProxy()->isArchived())) {
         $panel->addClass('project-panel-hidden');
       }
 
@@ -693,7 +701,12 @@
     $hide_uri = $this->getApplicationURI($hide_uri);
     $hide_uri = $this->getURIWithState($hide_uri);
 
-    if (!$column->isHidden()) {
+    $proxy = $column->getProxy();
+    if ($proxy && $proxy->isMilestone()) {
+      // You can't hide / show milestone columns manually;
+      // instead their visibility is based on the milestone's
+      // status (active / archived).
+    } else if (!$column->isHidden()) {
       $column_items[] = id(new PhabricatorActionView())
         ->setName(pht('Hide Column'))
         ->setIcon('fa-eye-slash')