Learn English – Can “real” be used as an adverb to describe an adjective

No native speaker of BrE would normally say Yes, I’ve got in that context. The reply might, as you say, be Yes, I have or Yes, I’ve got a pencil depending on the circumstances. A further possibility, in BrE as well is in AmE, is certainly Yes, I do.

I agree that using the word "too" makes a big difference in this sentence. It's perfectly acceptable to my ear to say "It's too cool over here" in a context in which warmth is expected. In this case, I might also use the phrase "It's cold over here" to mean the same thing as "too cool" because it is supposed to be warm or hot. "It's too cold over here" would be most acceptable if I expected it to be cool.

Basically, I think English speakers would consider air temperature "cool" to be in the 60s Fahrenheit, and "cold" to be closer to 40F. For liquids (for which internal body temperature is usually the basis for comparison, such as hot drinks or a swimming pool), I would think 80s for "cool" (e.g. below body temp), and cold starting in the low 70sF. Of course, if you're thinking of cold drinks, I would consider a soda "warm" if it was 70F.

Once you use the word "too," however, you are now talking more about personal perception than actual temperature.

You might also consider using the word "chilly," which generally connotes "uncomfortably cool," as opposed to "uncomfortably cold." I don't think of "chilly" as tied specifically to a temperature, more to a personal preference and contrast with what is expected or preferred.