Everywhere i have worked so far (office work) the holiday planning was made just by communicating with your colleagues. You just find a compromise that works for everybody. (Although there is a mentality of "first come, first serve". If you really need a holiday at a specific time, then better state it early, so the others can plan around it.) The official holiday request afterwards is just a formality, because everything is already planned through and the boss has no reason to decline it.

I am sure there are workplaces where it is handled differently, but that is my personal experience as an office worker.