There are opinions for and against this correlation. Cognitive functions are ways in whom our brain perceive and process the information. This process of our brain and our usage of different cells, parts, sides of the brain reflects in our fecial and body expression, so the usage can be visible. But there are opinions that controvert correlation to personality. If the brain uses different functions, that have different approaches to reality and that different approaches reflect on the outside behavior of body, or face is the personality correlation missing, is it there? Do functions and their approaches create a real personality type, or not?
This is a great question. My personal thought is that CT does contribute a significant "slice" of the pie that is our personality, but since it's not the only contributor, we can't truly draw a 1:1 relationship.
I think, when it comes to personality, the largest contributing factor is probably nurture... specifically, one's first years of life and home/family life. I'm just armchairing here, but maybe something like: