What is the right course of action here?

Your answer is fully correct. According to German traffic rules, when approaching a pedestrian crossing, especially in snowy conditions where road markings may be less visible, you must brake carefully and allow pedestrians to cross safely. Pedestrians on the right at a pedestrian crossing always have priority. It is important to reduce speed and be prepared to stop to ensure their safety. Continuing to drive without slowing down or yielding is not allowed, even if the road markings are hard to see due to snow. This rule helps protect vulnerable road users and prevents accidents.