OK, let's be honest: Mr. Rewrite created this post as an excuse to share his cool panorama of last night's dust storm. He's ever so proud of the shot. But let's find a reason to pretend he isn't showing off ...
Here's one: Mr. Rewrite disagrees with those who refer to dust-storm warnings. There's no reason to hyphenate it, at least in Mr. Rewrite's humble opinion.
The general rule on compound, or phrasal, adjectives is this: Hyphenate to avoid giving the reader the erroneous idea that the compound constitutes a noun (e.g. 13-year-old court-ordered busing plan, per an example from Garner's Modern American Usage).
Dust storm is a commonly used noun, as is health care. So one needn't hyphenate health care plan or dust storm warning.
Some organizations simply hyphenate every compound, even when the compound is a common noun. If that's their rule and they're consistent, more power to them. Mr. Rewrite will grit his teeth and move on, as he does when he sees this in his newspaper:
Mr. Rewrite leans heavily on the AP Stylebook here. It says to minimize the use of hyphens and to use them with the goal of minimizing confusion with compound adjectives (e.g. small-business owner). AP, for example, calls for health care in all uses.
Did you know that that wall of dust is called a haboob? One doesn't have to hyphenate that, so it could be a useful substitute ("The National Weather Service has issued a haboob warning!"), but Mr. Rewrite can't type it without giggling.