没有....+形容词= less...than 广东没有北京冷！Guandong is less cold than Beijing. 有...+形容词=more...thant 你有他高吗？ Is he taller than him? 我没有你游泳的好！My swim is worse than yours

有/没有 does not always mean has or have/not in the sentences. It depends. When 有/没有 + sbd. or sth. + complement ( often it is a adjective or adverb but a clause is also OK ), it indicates someone or sth is/is not comparable to someone or sth. E.g. 广东没有北京冷= Guangdong is not colder than Beijing/ Guangdong is not as cold as Beijing. 你有他高吗？= Are you as tall as him?

有/没有+adj=more/less+ than

here "没有" means "not as ... as ..."

if to translate directly 广东 没有 北京 冷！ = Guanzhou hasn't Beijing's cold 你 有 他 高 吗？= do you have his height? 我 没有 你 游泳 的 好！= i don't have your skill for swimming it's the meaning of possession everywhere it's just possession of degree, not posession of an object