The color change could be caused by the seasons, in winter they all get white and turn back to their natural color in summer. Also, animals can only die trough attacks from predators (fox/wolf/bear) or through not enough light. This means you will have to have some kind of light source to prevent them from despawning. It will show in the Block Info HUD if an animal will vanish because of that. Sunlight also prevents them from vanishing, so keeping them outside should be enough.
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C_Man's post in Do animals age on their own? was marked as the answer