Right now there is Frozen Fun even at DCA, but much of it will be over by the time June roles around. I think the only things you can be pretty sure will still be happening in June are the Anna & Elsa meet and greet (DCA) and the Frozen show at the Royal Theatre (DL) (thought it might be alternating with Tangled and Beauty and the Beast by that point). They have added Arendelle to the Storybook Canal attraction, so that should still be there. Also, the A&E pre-parade float appears to be running ahead of Soundsational, so if that parade is still running in June, that might be another chance to see them.
Unfortunately, the Sing-A-Long, Olaf's Snow Fest, and Freeze the Night are slated to end before June. They may extend them "due to popular" demand, but so far there are no rumors/indication that they are planning to do so. I wouldn't be surprised if the Olaf Meet and Greet continues in some fashion, but at this point, that's slated to end April 30. The other two activities are slated to end on May 15, just before the kick-off to the 60th anniversary.