General rules in negative adjectives in superpolite form

Question

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 word, 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 this cases?

Answer 1

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.

Answer 2

寒くないございます is ungrammatical. 寒くございません/寒くはございません　is grammatically correct.