First, just look at what can be done with paper as the primary material. This could either be a prototype for something later made in metal or wood, or this could be the finished product. Worried about longevity? I have seen a paper/cardboard automaton from the 18th Century that works just fine today.
Second, behold the power of well-considered linkages. The entire complex sequence of motions is driven from a single offset crank in the center of the horse. Very subtle movements, such as the head, are secondary motions. The interdependence of large and small motions gives the horse a very lifelike quality.
Third, while automata may be made of tangibles such as wood, paper, and metal, there is good reason to consider Computer Assisted Design (CAD) when creating them.
Check out some books on Mechanical Linkages, Paper Engineering, and Learning CAD.