To tease, banter with, or make fun of someone (often playfully or mockingly).
友達に彼女ができたと聞いて、みんなに冷やかされた。
When my friends heard I had a girlfriend, everyone teased me about it.
彼は恥ずかしがり屋なので、すぐ冷やかされる。
He's shy, so people tease him easily.
冗談半分に冷やかすつもりだったが、不愉快にさせてしまった。
I meant to tease half in jest, but I ended up making them uncomfortable.
To cool or refrigerate (somewhat archaic/rare usage); modern Japanese more commonly uses 冷やす for this meaning.
夏には酒を冷やかして飲むのが好きだ（やや古風な表現）。
In summer I like to chill the sake and drink it (somewhat old-fashioned expression).
出された料理を冷やかすという表現は現代ではあまり使わない。
The expression 'to cool the served dish' using 冷やかす is not often used in modern language.
To look around a shop without buying; to window-shop or browse with no intention to purchase.
休日は友達と街を冷やかして歩くだけだった。
On my day off I just strolled around town window-shopping with friends.
試しに入った店を冷やかして回っただけで買わなかった。
I just looked around the shops I walked into and didn't buy anything.