When I think back to the popular Japanese songs that sing about "fog," I'm surprised at how many there are. I remembered 19 songs. It's no fun to list them from memory, so I'll look into waka and haiku poems that Japanese people have written about "fog."
To begin with, I looked closely at the Kokin Wakashū (古今和歌集;Collection of Ancient and Modern Poetry, 905) and found nine poems in which about “fog”, two of which were by known authors and the rest were anonymous.
恋こいて逢う夜は今宵天の川霧立ちわたり明けずもあらん
The night we meet longing for each other tonight the Milky Way will be covered in mist it will probably never dawn
春霞かすみて去にし雁がねは今ぞ鳴くなる秋霧の上に
The geese that left in the spring mist for the northern country are now returning here as the autumn mist rolls in
人の見る事や苦しき女郎花秋霧にのみ立ち隠るらん 壬生忠峯
Embarrassed to be by people Ominaeshi flowers stands probably hidden in the autumn mist
Mibu no Tadamine
霧たちて雁ぞ鳴くなる片岡の朝の原は紅葉しぬらん
The mist rises and the geese cry The autumn leaves of the morning fields of Kataoka must be at their best right now
[Note] Kataoka is currently near Oji-cho, Kitakatsuragi-gun, Nara Prefecture.
秋霧は今朝はな立ちそ佐保山の端はその紅葉他所にても見ん
There must be a lot of mist around the edge of Mount Sahoyama this morning The autumn leaves there are beautiful but I'll look elsewhere
[Note] Mt. Sahoyama is currently around Saho in Nara City.
秋霧の共に立ち出でて別れなば晴れぬ思いに恋や渡らん 平元規 蔵人右衛門尉
The morning dawned, autumn mist rolled in We stood up together, time to say goodbye but just as the mist did not clear my feelings for you did not clear either and my love for you only grew wider
Taira no Motonori, Kuroudo no Uemonnojo
ほのぼのと明石の浦のささ霧に島隠れ行く舟をしぞ思う
As dawn breaks the gentle mist of Akashi Bay I watche the boat gradually disappear behind a small island I think of the person I love
朝な朝な立つ河霧の空にのみ浮きて思いのある世なりけり
Every morning the river mist rises and floats in the air It floats and leaves thoughts of this sad world
秋霧の晴れて曇れば女郎花花の姿ぞ見え隠れする
Just when I think the autumn mist has cleared the sky becomes cloudy and the Ominaeshi flower can be seen but then it disappears again
When we look at these nine poems in this way, we can see that "fog" as a natural phenomenon is given a metaphorical role of hiding or revealing things, and that it generally symbolizes "love." In other words, the poems are not about a misty scene in and of itself. They are about entrusting a more depressing emotion to the fog. But has this emotion entrusted to the fog continued into much later times?
When I searched for haiku by Matsuo Basho (1644-1694), written about fog about 750 years after the compilation of the Kokin Wakashu, I found one in "Nozarashi Kiko (野ざらし紀行)“ 1685-87. There is also one in "Sarashina Kiko(更科紀行)”1688-89, but this was written by Ochi Etsujin (1655/56-?) who accompanied Basho on his travels. Let's take a look at these two poems.
霧しぐれ富士を見ぬ日ぞ面白き 芭蕉
It's interesting to see the mist and rain especially since you can't see Fuji Basho
(During the journey, Mt. Fuji never disappeared from view, so when the mist and rain fell and Fuji disappeared, it was a special pleasure.)
霧晴れて棧は目もふさがれず 越人
The fog has cleared, so the shoji screens are left uncovered with windproof Etsujin
These two poems do not have the slightest bit of emotion found in the Kokin Wakashu. Romance is out of the question.
Matsue Ishu Shigeyori (1602-1680), about 40 years older than Basho, was said to be a heretic in the Teimon school of haiku, but his book "Kebukigusa (毛吹草)”1645, was widely used when Teimon school of haiku was in its heyday and was a masterpiece. "Kebukigusa” contains "Haiku Shiki no Kotoba (俳諧四季之詞),” which can be called a collection of seasonal words, and in the "Autumn" section there is "Mist." If we include the later "additions," there are eight poems about fog. We will look at them below, but in fact even the Teimon haikai that preceded Matsuo Basho no longer had the sentiment of ancient and modern times. So, is it a calm observation of fog as a natural phenomenon? Well, we can say yes, but we can't say no. If waka is the high-brow literary art of the aristocracy and samurai classes, what was emerging here was a new literary art called "haikai" that somehow evoked the humorous spirit of townspeople. It is different from the interest in serenity that is connected to the "wabi" perfected by Basho, and can be said to be a perspective on nature and things that is the very preliminary stage.
Anyway, let's look at the eight poems from the "Fog" section of "Kebukigusa.” There is no need to interpret them, so I will leave that out.
是はまた霧を通すや風袋 重頼
Noway, this is a wrapping that not the wind but the fog through too Shigeyori
霧の海に立つや白鷺の波頭 道二
A white heron standing in a sea of mist, the crest of a wave Douji
富士は磯というや理霧の海 重方
Mt. Fuji is called a rocky shore! standing over the sea of mist Shigekata
風の手のやふるや霧のまばら垣 正依
The wind's army blows mist arrows into the sparse hedges Masayori
(I will give my own interpretation of this phrase. The wind's hand falls on the sparsely fogged fence. Also, as an alternative interpretation, the wind's hand breaks through the sparsely fogged fence. The latter may be more natural.)
大海を手柏で急く霧間かな 正直
It is like the ocean, must I harry to go with clapping my hands through the mist Masanao
天は沖地は磯なれや霧の海 未得
The sky is the ocean, the earth is a shore, the sea of fog Mitoku
風口は干潟となるや霧の海 不及
When the wind turns into a tidal flat the fog turns into the sea Fukyu
朝霧の海高くして山もなし 一言
The sea of morning fog is high but there are no mountains Ichigen