¿Cuál es la diferencia entre さむい y つめたい ?Puedes dar oraciones como ejemplo.

The former words "さむい（寒い）" means low or cold temperature and you can't use Person and person's name as the subject. Normally, the location's name, place's name are used for subject.
The latter"つめたい（冷たい） " means "Cold".
This word is an adjective, so you can use this words anything including items and person.
But, you should avoid using this word for particular person and people because the phrase"つめたい（冷たい）ひと(人)" is used to accuse the person who have cold, impassive, chilly heart person and so on.

Example

さむい(寒い)
・きょう（今日）は寒いな。
(It's cold (temperature) today.)


つめたい（冷たい）

・このかわ（川）のみず（水）は冷たい
(The liver's water is cold)
・あなたは冷たい人だ
（You're a cold-heart person）

That's all.
Go for it your study.