Is a bonnet a hat for a guy or a gal? ... In American English a bonnet is usually a large brimmed hat for a woman or girl. In some parts of the U.S. it is becoming exclusively associated with Spring time or Easter.
Look up the Balmoral Bonnet or the Tam o' Shanter. It's a traditional Highlands/Islands flat cap. In the States we'd say it looks kind of like a beret.
I wrote "It is cold, put a bonnet on", which was marked wrong. Is this a context issue or is my understanding incorrect?
I think because it says 'air' which is 'on him' from that on then knows it must be 'he is cold'