If a ride goes down during your FP time slot you're sent an email telling you it's down and you'll see a list of available rides that you can use an anytime FP on for the remainder of that day. However it has to be during your original FP time slot or later. So if you have Big Thunder and it goes down and you have it FP'ed for 2pm. You can use your anytime FP from 2pm until park close.
This is what the email you get looks like. Note that it's not every ride in the park, it's select rides. And you can also use the anytime FP for your original ride if it happens to start operating later that day..that is if you haven't used it on one of the other rides
With the Frozen ride, since it's brand new and there's a lot of demand and it's been going down quite a bit. It seems like they've been offering an anytime fast pass that's good for that day or the next couple days. It's still a one time use, but being that it might not be back up that day they want to give those the option for it for another day. So they've been a little more generous for that ride. That's really been the only exception. All other rides expect to just see the email.