Gelid \ جليد
is a Latin\Arabic word that means ( ice ) in English, which is a perfectly good name for Ice Bath business.
is a Latin\Arabic word that means ( ice ) in English, which is a perfectly good name for Ice Bath business.
The logo concept is a ( fan ) which gives us a cool & breezy feeling and it also describes the ice bath which is also "cool & breezy".
Then I took the letter "g" which is the first letter of the world "gelid" and combined them as below: