The Adjacent Tooth to the Implant Have Receding Gum and Suffer from Pain with Cold and Even Ordinary Water?

You have to get the site evaluated 

The Xray of the site will show if there is any bone loss adjacent to the tooth and implant 

this will dictate if the recession could be corrected and if the exposed root could be completely covered. 

Sometimes , 100% root coverage is not possible.   Therefore, after tissue grafting,  desensitizers, and resin bondings could be used to reduce sensitivity and protect the exposed root 

You should make an appointment with your dentist to have an Xray taken. It is very important to monitor the bone level around the implant and adjacent teeth. Depending on what the xray reveals, treatment options can be discussed.