[Supperman]

1. このことは今度お目にかかった折に詳しくお話しいたし ます。
2. 先月北海道に行った折、偶然昔の友達に会った。
3. 何かの折にわたしのことを思い出したら手紙をください ね。
4. 寒さ厳しい折(である）から、くれぐれもお体を大切に� �てくださ い。

折
≒時
≒time,
when,
the time when,
occasion,
incidence

「あるいい機会に」という意味で使われることが多いから、後の文には マイナスのことがらはあまり来ない。
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My literal translations;

1. I will make a further explanation about this matter, when I meet you in person next time. (when・・・next time = 折）

2. I met one of my old friend by chance, when I went to Hokkaido last month.

3. Please send me mail in such an occasion when you remind of me.

4.Please take good care of yourself, as it is the time/season when the climate is awfully cold.

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My translations are just like yours.

1. When you look at this thing next time, we will talk in detail.
2. When I went to Hokkaido last month, I bumped into an old friend.
3. At some point, if you think of me, write me a letter, OK?
4. When the cold is brutal, please take care of your body [yourself].

The purple bold words in your sentences are equivalent to "折".