What is the right course of action here?

In this scenario, the correct actions as per German traffic rules would involve two key points:

1. You must brake carefully. This is crucial in snowy or icy conditions where traction may be reduced. Rapid braking can lead to skidding, so a smooth and gradual application of brakes is essential.

2. You should allow the pedestrian on the right to cross the road. Pedestrian priority is a fundamental rule in German traffic law, especially at crossings. Even though there might not be marked crossing points, pedestrians still have the right to cross whenever it is safe.

This combination ensures that you prioritize safety for both yourself and pedestrians, adhering to the principles of responsible driving and pedestrian rights in Germany.