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I have trouble trying to find this specific grammar in text books.
I have a negative adjective in polite form:
寒くないです
I want to use the superpolite form:
寒くないございます
That seems right, but I have seen in a grammar book that when using other words, they replace the い with う, like this:
面白うございます
Is the first example correct? If not, what is the general rule to apply in these cases?
This is a bit tricky.
I would first of all suggest you never use お寒うございます at all.
The key to understanding this is understanding what this form really is.
It is from classical Japanese. In modern Japanese it's usage is restricted to this set. This is primarily used as greeting between older people. There is no negative form in modern Japanese.
In classical Japanese the negative of 寒うござる would effectively have been 寒うござらん or 寒うごらざぬ. The う can be considered to have the same effect as く in modern Japanese so 寒うない may have also been used at some times.
Without reading a body of classical texts, it is impossible to be sure what was considered to be "correct" in any given period. However it is clear that there is no modern negative equivalent of this form. Use either a positive adjective that effectively negates it, such as [暑]{あつ}う or use ～くありません.
寒くないis not in polite form. (2)寒くないございますus ungrammatical. (3) Your third example is about ウ音便. Look into that. There is not difference between negative forms (which itself is an i-adjective) and other i-adjectives. – user458 Jan 4 '12 at 12:29寒くないです? Polite, neutral? – Alberto Fernández Jan 4 '12 at 12:44寒くないですis polite form (for less educated people or informal use). A better form is寒くありません. – user458 Jan 4 '12 at 19:28