Learn Turkish: Soğuğa rağmen yüzüyorlar mı? - Are they swimming despite the cold?

The postposition rağmen (despite) requires the word before it to take the dative case (-a or -e suffix). You can think of it as saying "despite to the cold".

Where did the ğ in soğuğa come from? Isn't the word for cold soğuk?

Yes, the root word is soğuk. When a Turkish word ends in a hard k and receives a suffix starting with a vowel (like the dative -a), the k softens into a ğ (soft g). This is a very common spelling rule called consonant mutation.

I thought soğuk was an adjective. How can it take a noun suffix like the dative case?

In Turkish, adjectives can easily act as nouns depending on the context, without needing an extra word like "one" or "weather." Here, soğuk means "the cold" as a noun, which allows it to take noun suffixes.

Could we place the question particle mı after rağmen instead?

Yes, but it changes the focus. Placing mı at the end makes it a neutral question: "Are they swimming?" If you say Soğuğa rağmen mi yüzüyorlar?, you are emphasizing the condition: "Is it despite the cold that they are swimming?"