Hi there
The rotator cuff consist out of four muscles and several tendons that form a covering around the top of the upper arm bone (humerus).
These muscles form a cover around the head of the humerus under the deltoid.
The rotator cuff holds the humerus in place in the shoulder joint and enables the arm to rotate.
Rotator cuff tear is a common cause of pain and disability among adults. Most tears occur in the supraspinatus muscle, but other tendons and muscles may be involved such as the tendon of the long head of the biceps.
The cold feeling does not seem to be related to tendon, ligament or muscle but, rather, to nerves.
I think you have a nerve impediment in the thoracic spine, at T1-2 and 2-3 level and would be advised to see a chiropractor familiar with Applied Kinesiology (AK)
The nerve affected in this spinal segment also controls the function of the subscapularis, and the heart, and having this spinal segment adjusted would prevent a lot of problems later in life.
Good luck
Kinetico