Here are the examples of adjectival intensification:
It's quite cold here in March.
It's pretty cold here in March.
It's fairly cold here in March.
It's rather cold here in March.
To me, their meaning seems altogether the same—It's cold to a slight or medium degree, a little more or a bit less— but I doubt about the exact sameness.
To make the question topical, I should explain that it was brought up during one of the numerous wide-ranging discussions on the subtleties of the English language I had a few days ago with an acquaintance of mine. Then, he claimed that all intensifiers, even those in my examples, can be ranked by their strength, and backing his point, he mentioned a book on adjective intensification he had come across when he studied the English Language at the University (not in the English-speaking country) in the early 2000s.
After a painstaking search, I came across a link to a book which is unavailable in the place I live in. When I sent the link to the man, he said that the book's title seems familiar to him, but he's not sure.
So, my question is:
Is it true that the intensifiers in the examples can be ranked by their strength? If it is true, what might be their descending order? If there's no rule for this, is there a customary usage order?