While overtaking a cyclist in conditions of limited visibility, outside a built-up area, should you use short horn signals?

Yes, in the situation shown, such an obligation exists. According to Art. 30 para. 1 pt. 1 lit. b of the Road Traffic Act, when driving in conditions of reduced visibility (e.g. fog), the driver of a motor vehicle outside a built-up area must give short audible signals when overtaking. The purpose of this regulation is to warn another road user about the manoeuvre being performed, which is crucial for safety in limited visibility.