Is the word norte the same in Brazilian and European Portuguese?

Yes

The word "norte" is identical in meaning, spelling, and grammatical function in both Brazilian and European Portuguese. The only difference is in pronunciation:

• Brazilian Portuguese: The vowels are generally more open, and the final "e" is often pronounced as a subtle "i" (e.g., nor-chee).
• European Portuguese: The vowels are more closed or reduced, and the final "e" is often nearly silent or very short (e.g., nort').

Brazilian Portuguese Examples

1. Eu vou viajar para o norte do Brasil. (I am going to travel to the north of Brazil.)
2. Ele está meio sem norte na vida. (He is a bit directionless in life.)
3. A bússola aponta para o norte. (The compass points north.)
4. O norte do país é muito quente. (The north of the country is very hot.)
5. Eu estou precisando de um norte para o meu trabalho. (I am needing some direction for my work.)

European Portuguese Examples

1. Vou viajar para o norte de Portugal. (I am going to travel to the north of Portugal.)
2. Ele encontra-se sem norte na vida. (He finds himself without direction in life.)
3. A bússola indica o norte. (The compass indicates the north.)
4. O norte do país é bastante fresco. (The north of the country is quite cool.)
5. Preciso de um norte para o meu trabalho. (I need some direction for my work.)