Consider the following premises. It is cold if and only if Richard is sleeping. If it is cold, then it is windy. If it is windy, then Richard is sleeping. Can we infer the following from them? It is windy if and only if it is cold.
 From the fact that it is cold if and only if Richard is sleeping we can infer that if Richard sleeps, then it is cold. From the fact that if it is windy, then Richard is sleeping, and that if Richard sleeps, then it is cold we can infer that if it is windy, then it is cold. Finally, from the fact that if it is windy, then it is cold, and that if it is cold, then it is windy we can infer that it is windy if and only if it is cold. Therefore, the answer is yes.