Based on the level of respect or formality, you can say "It's foggy" in Korean in 3 ways:

• Informal: angae-ggin nalssi-ya (안개낀 날씨야)
• Formal: angae-ggin nalssi-yeyo (안개낀 날씨예요)
• Very formal: angae-ggin nalssi-imnida (안개낀 날씨입니다)