I worried about my cats and dogs when I had ice on my pond, too! They would reach out there and get a drink where I had the bubbler. Sorry to hear about the little doe, but she will be fine. Your fish is likely just hanging between that rock, pretty unlikely that it got hurt, and I will sure hope all is well! Since I have no ice, I can see all my fish (haha, all 31 of them, shame on me!) and the koi seem to hang low when the water and air temps are cold, but as soon as the sun comes out and warms the higher water, they will come up to about halfway in depth. The goldfish on the other hand seem to mill about much more than the koi. Goldies will nibble on the sides and so forth.
Someone posted in another thread about the turning over of ponds, and one thing I remember is that a hard long winter with snow cover on large ponds (and I assume our koi/goldfish ponds would be included) made it much more dangerous for the fish. Obviously, the fish can stand the frozen ponds. It's the number that we sometimes have in the small areas that makes it more dangerous to not have an opening to let gases dissipate. But, the thing about the snow, it said that if snow could be removed safely, it should be so the sun can reach through the ice, and that helped with the turn over not being so drastic. Just a thought, but obviously not something to do unless ice was very thick and it was safe to remove the snow.