This answer is based upon the etiquette I've been taught and always heard since childhood. Its rule have been followed for decades by people I know/met, and I've seen it used in Western Europe countries (Belgium, France, Germany1). The Netherlands being so close to those countries, it might apply here too I believe2.
So: sending greetings/Christmas cards was first introduced by Sir Henry Cole. At that time, it was common thing that a letter would take up to a month to reach its recipient. So, nothing rude in being wished a Happy New Year on January 28th for instance. As far as I know, this custom has been kept: when you meet people for the first time since January 1st, and until January 31st, you can wish them a Happy new Year. After that, it seems really outdated, and a bit weird, as people would think you had forgotten about them. This can apply to foreigners too.
At the workplace, I've seen the same rule apply, with a small adjustment, because of "crossing holidays", people coming back to work on different days: after a week, no more Happy new Year, it's annoying and useless. Unless you're a big company, and you meet people once in a while in another office, where same standard one-month-rule applies.
Note: I've always been taught that, as a child, you are the one that should show "more" respect to elderly people (in the sense of "doing it first"). I've done that too at the workplace. Don't wait for your director to send his card/email/wishes, be proactive. And it'll lift the burden of answering too :)
I'm no more a child, but I'm still doing that. Write first when possible. Even with employees (almost mandatory here, because I include a gift card/box, so it has to be a couple of days before the day/vacation). Still, it's not out of the etiquette or weird.
1. when in England, we would do it the same way as in our countries (many different nationalities working in London), but I realize now that native British do it until December 25th and usually not later, it never crossed my mind maybe because they adapted their greetings to us, foreigners.
2. citation from Dutch people to confirm this would be great here.