The reasoning was talked about in the docs that your ortho sent you. In short, inflammation and compression of the trigeminal nerve leads to a host of neurological issues.

@TGW liek what else can it affect? I know a friend with cold feet and his jaw is misaligned some also tend to think hes strange i wonder if that plays a factor

That's..complicated and I'm not up to a full answer because it is so complicated. A simple explanation though, is that jaw alignment is secondary. The face is a reflection of the airway. In some people the neurology of airway compromise causes havoc in the autonomic nervous system leading to sympathetic dominance. This leads to poor peripheral circulation - the body thinks it's in a constant state of 'dealing with threat' and alters blood flow to be prepared for dealing with that 'threat'. With PNS outflow you get better blow flood, SNS outflow, tends to vasocontrict; note that whether it goes one way or the other and leads to cold hands and feet is more than just which ANS branch is active, they're both active all the time, it's about the balance between the two, how 'noisy' one branch of the ANS gets. Think of it like having two sides of a debate - they can speak calimy and have a discussion, or yell at each other until neither side can get heard very well. In the chronic pain/airway patients, it's a yelling match. In the OSA patient, they've b een yelling so long they don't really listen, and have gone half-deaf from the niose to boot.

The reason airway compromise and chronic pain lead to cold hands and feet, and a varieyt of other issues with one's health, is it acts as a chronic stressor sensitizing the HPA-Axis. That's the key, and that's also why jaw pain patients, who experience chronic pain, can develop similar symptoms. Yet, I would go so far as to say most jaw pain patients (TMD) really have airway issues due to how their face developed. So, these two problems of chronic myofascial pain, compressed TMJs, and difficulty breathing are intertwined. For the odd patient whose facial development was relatively good and their airway not significantly compromised, the macrotrauma TMD patient as an example, they can develop cold hands and feet as well.

Could be due to being skinny as well. Skinny guys always have cold extremeties compared to fat people