good question!! in english, 涼しい is cool, and 寒い is cold. so 寒い is colder than 涼しい. you can say that 今年はとても寒い。 this winter is very cold. 今日は夏だけど少し涼しい。 it is a little bit cool although it is summer. 冷たい is a little bit different from 涼しい and 寒い when we use 涼しい and 寒い, we often describe about weather or climate. but 冷たい often describe something or temperature itself. example is best way to explain this!! このアイスクリームは冷たい。 this ice cream is cold. このビールは冷たい。 this beer is cold. sometimes we use 冷たい when we describe the person. 彼はいつも冷たい。 he is always cold. last example is; 今日は風が冷たいから、昨日は涼しかったけど、寒い。 It's cold today since the wind is cold although it was cool yesterday. I hope I can help you.

Agree with kota. 凉しい 凉爽 用于天气 冷たい 冷的，冷淡的 用于物体的温度、人的态度 寒い 寒冷的 同样用于天气，也有用为 无聊的，不好笑的 ，就是所谓的 冷笑话 。