As Dean pointed out, this was an incompatible change.

This reverts commit 0cab76ae.

core/src/main/java/hudson/EnvVars.java

@@ -185,7 +185,7 @@ public class EnvVars extends TreeMap<String,String> {
      * when we later kill the processes.
      */
     public static EnvVars createCookie() {
-        return new EnvVars("JENKINS_COOKIE", UUID.randomUUID().toString());
+        return new EnvVars("HUDSON_COOKIE", UUID.randomUUID().toString());
     }
 
     /**