冷たい means "cold, chilly" (low temperature) and it can be used also to describe people and then it means cold as "unfeeling". It usually describes something in neutral or negative meaning. Example from the first meaning: 冷たい風 (chilly wind), and from the second: 心の冷たい人 (cold-hearted person). 涼しい means "cool, refreshing" and it has positive meaning, as in 涼しい風 (refreshing breeze). It can also mean "cool/refreshing looking". I hope this helps! :)

Remember that one cannot say 外が冷たい (meaning "it's cold outside"),　冷たい is only used for objects, not for weather. To describe cold weather in Japanese there is a different adjective - 寒い.