What is the difference between мне холодно and я замёрзла ?Feel free to just provide example sentences.

It has little to zero differense in meaning. You should look for how they differ grammatically.
The point is that "мне холодно" is an Impersonal construction in russian (it has no subject).
Холодно = it's cold
Мне холодно = I (personally) feel that it's cold
Ему холодно = He (personally) feels that it's cold
etc
When talking about the past or the future you'll need additional words:
Вчера мне было холодно - I was cold yesterday
Думаю мне будет холодно в футболке - I think I'll be cold in a t-shirt

"Я замёрзла" is a personal construction (has subject, which is "Я") in the past tense, but you can use it in present, meaning something like "i felt that it's cold for some time, but i'm telling you/realizing this only now". You don't need any other words to say this in past - "(вчера) я замёрзла", but you CAN'T use this exact phrase in the future tense. To do this you'll need to change the form of the verb "замёрзла" from past to future tense.

So my advice would be to learn more about Impersonal constructions. They are a big part of the russian language and this topic is too big to explain in short.

Examples:
Я давно здесь стою, и мне холодно. - Я давно стою здесь и замёрзла.
Я промокла под дождем, поэтому мне очень холодно.
Мне холодно, и я хочу поскорее попасть домой. - Я замёрзла и хочу поскорее попасть домой.
Если не хочешь, чтобы я замёрзла, приходи быстрее.
Я замёрзла, подай, пожалуйста, куртку. - Мне холодно, подай, пожалуйста, куртку.

(as you can see they're interchangeable in most cases)
HTH~