冷, 寒, 凍

冷たい
Tsumetai
E.g.
風が冷たい。
手が冷たい。
(Some specific thing is cold)

寒い
Samui
E.g.
今日は寒い。(feeling cold in general)
今日は冷たい <--- Is incorrect. 今日 is not a specific thing.

私は寒い。(feeling cold)
私は冷たい <--- This mean you are saying you are a cold person.

凍てついた足 (this is colder than cold, freezing!)
My feet were freezing
風が冷たくて、私は凍るほど寒い。
The is cold so I am freezing.

*Thanks to Mitsue Kawashima Sensei! :-)