さむい (samui) : use when you feel cold in the weather 冷たい (tsumetai)　: use when you eat, drink something cold. it also be used when someone behave to you by the cool way.

The weather is cold and you feel cold: さむいです。 About the personality, though it's a negative expression, "I'm a cold person": わたしはつめたい(にんげん)です。

さむい (samui) - I'm cold

You would say さむいです