「厳{きび}しい寒{さむ}さの中{なか}、水中{すいちゅう}で綱{あみ}を引{ひ}き豊漁{ほうりょう}を祈願{きがん}する伝統{でんとう}の神事{しんじ}が、福井県美浜町{ふくいけんみはまちょう}で行{おこな}われました。」
This sentence is perfect in every way.
If you inserted 「で」 after 「寒さの中」, the sentence would still be grammatical but it would sound a little more conversational when it clearly is not meant to be. 「で」 would be redundant in this context -- more so than you might think.
When talking about an event taking place in a meteorological condition, a general ambience or a psychological state in a non-conversational setting, using 「で」 would often make the sentence sound less than great.
The reason for using a comma after 「寒さの中」 should mainly be for clarity. It prevents us from having to see a funny-looking 「中水中」 in the 中 of the sentence. No 親父{おやじ}ギャグ intended.