If any of these animals are not there, look around the surrounding area. If they still do not appear, go to the farthest away town (Empire or Dodge) and return.

Gray Wolf: Near the bridge in Dodge.
White Buffalo: Near the mine (not Magruder's). It roams with the other buffalo.
White Wolf: Near Piper lake, usually by the waterfall.
Mountain Lion: Go to where Magruder's mine is located. Stand at it with your back to it. To your left is the train tunnel, and to your right is the path to the Indian hunter. Go through the middle path and it should be through there.
Great Wolf: Same place the White Buffalo was, usually behind the mine.
Grizzly: Near Empire.The map will show you its location. You do not have to use an arrow to kill him.