Learn Dutch: Ik zal je omhelzen om de koude te vergeten. - I will embrace you to forget the coldness.

You are right that de kou is the common everyday word for the cold. By adding the suffix -de to the adjective koud, you create the abstract noun koude (coldness). This form sounds more formal, literary, or poetic, which perfectly matches the romantic tone of this sentence.

What is the difference between omhelzen and knuffelen?

Both mean to hug or embrace, but they have different nuances. Knuffelen is the cozy, everyday word for hugging or cuddling. Omhelzen literally means to put your arms around someone (an embrace). It is slightly more formal and dramatic, pairing nicely with the poetic use of koude.

Could I leave out the word om and just say je omhelzen de koude te vergeten?

No, because you are expressing the purpose of the embrace. When you want to say 'in order to' do something in Dutch, you must use the om ... te + infinitive structure. Leaving out om would make the sentence ungrammatical here.

Why do the verbs omhelzen and vergeten both sit at the end of their respective phrases?