The expression make hay has a few definitions. First, it’s short for the proverb make hay while the sun shines. Hay is difficult to prepare in wet weather, so the proverb points to the wisdom of taking advantage of opportunities while they’re available. Second, make hay means to turn [something] to one’s advantage.
This newer sense derives from the first one, perhaps originally out of confusion over the meaning of the metaphor, and it involves making hay out of something specified. In the first sense, what the hay is made of isn’t relevant.
The Oxford English Dictionary lists another sense of make hay of: “to throw into confusion.” But we find no examples of this sense put to use in recent sources.
When make hay is in its first sense—highlighting the wisdom of taking advantage of opportunities while you can—it’s usually embedded in some form of the proverb:
They retain the edge in terms of pace but there can be no more off-days if Hamilton and Button are to make hay when the sun shines. [Daily Mail]
Their objective, after all, is to make hay while the sun shines, and it shines less brightly with the cloud of apology in the way. [Newsday]
They should make hay while the sun was shining. [Guardian]
But make hay is much more often used to mean to turn to one’s advantage, as in these cases:
Republicans are trying to make hay out of comments Joe Biden made while campaigning in Ohio last week. [Boston Globe]
Hedge funds made hay with trades that shorted the dollar and went long on commodities. [Reuters]
Labor has been making hay with the family’s complicated and diverse business dealings. [The Australian]