What is the real difference between the proper use of the words さむい and つめたい?

In English it seems that cold is just always cold just as warm and hot regardless of whether the word describes a person's experience or the actual physical state of an object. In Japanese however there seems to be a strange case where when describing a cold weather versus a cold drink you would use the words [寒]{さむ}い or [冷]{つめ}たい respectively, which both seem to translate to the word cold in English. This difference has always been confusing to me and I can't seem to develop a rule-of-thumb to follow in order to choose the right word for the right situation.

I've heard it described by some native Japanese speakers that 寒い should be used for things that you cannot touch. My assumption is that by "cannot touch" this is referring to things in a more abstract concept such as weather or the day and not things that are simply out of reach physically such as a distant planet, however I haven't been able to confirm the last case.

Another point that I think is interesting is that the words warm and hot in English do not seem to have the same Japanese word counterparts where one is more direct translation and the other means "to the touch" but instead warm and hot in Japanese appear to be simply あたたかい and あつい respectively. Am I missing something, perhaps there are other word analogies for these other adjectives of which I'm just unaware.

As requested here are a few examples that demonstrate my confusion as far as proper usage of these two words.

• 空気は寒い when speaking of feeling of the air when stepping out of the house.


• 水は冷たい when wading through some cold water.


• 私はさむい when describing one's physical feeling caused by any of the above.

Answer

"冷たい" is used for physical objects that are cold to the touch.

• Ice is "冷たい". A surface is "冷たい". A person can be "冷たい". Water is "冷たい".

"寒い" is the feeling you get when cold, or something that causes that feeling.

• Weather is "寒い". You can get "寒い" after touching a "冷たい" thing. The atmosphere of a situation can be "寒い" (if many "冷たい" people are present).

水が冷たかったから私は寒いです。
'The water was cold, now I'm cold.'

"Warm" has the to-the-touch differentiation only in its writing. "熱い" is hotter than "暖かい". "暖かい" implies a good feeling usually, while "熱い" can mean unpleasantly hot.

• Weather is "暑い" or "暖かい", while coffee would be "熱い" or "温かい".