In this situation, are you obliged to keep a safe distance from the horse-drawn vehicle you are driving past?

Yes, you must maintain a safe distance during any passing manoeuvre. According to Art. 23 para. 1 pt. 2 of the Road Traffic Act, you should also reduce your speed if necessary. In the case of an animal-drawn vehicle, this is particularly important because an animal can behave unpredictably and, for example, suddenly change its course.