"Stand up one minute after the number of black hats you can see. So if, for example, you see seven black hats, stand up after eight minutes and announce your hat is black."
Why does this work? Let's simplify it (it's a recurring thing here).
If there were only two of you, and you know there must be at least one black hat and one white hat, you know you're wearing the exact opposite colour of the other pony and both of you will announce your hat correctly.
In the event of three ponies, there would be one of one hat's colour and two of the other. Let's imagine there's two black hats and one white. Anypony wearing a black hat will see one black and one white hat.
If you are wearing a white hat and you can see a black and white hat, the pony wearing the black hat will only see white hats and deduce she's wearing black. But if she only sees one black and one white hat, she won't stand up, not right away. This NON-action allows you to deduce that she can't work out what colour her hat is because she can see two colours and so you conclude you must be wearing black. This goes both ways. If neither of the other ponies stand up, after a while, they'll stand up at the same time.
You therefore need to introduce time intervals for a successful strategy related to hat identifying and use silence as a sort of signalling system, hence this strategy. If you can't see any black hats, stand up after one minute. If you see one, and the pony wearing it doesn't get up after one minute, stand up after two minutes, and so on.
It's a great strategy because there's pretty much no way for you to blow the entire thing by guessing wrong. If you're worried that if you see, say, twelve black hats and stand up after thirteen minutes thinking you're also wearing black, but it turns out white, don't worry.
In that case, whoever's wearing black hats would only see eleven black hats and stand up after TWELVE minutes. There wouldn't ever be a thirteenth minute for you to guess at!