How to check if a Carbon date object is at the start of day?

In the meanwhile its even easier. Use the is....() methods (see carbon comparison) like this:

$date = Carbon::now();
if($date->isStartOfDay()) {     // check if hour is 00:00:00
    // whatever
}

If you just want to check if it's the start of the day, then it's fairly easy to check with Carbon's startOfDay() modifier and a comparison:

$date = Carbon::now(); // or whatever you're using to set it
$start = $date->copy()->startOfDay();
if($date->eq($start)) {
    // do your formatting here
}