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

Yes

The word "inverno" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the vowels are generally more open and clearly articulated. In Continental Portuguese, the pronunciation is more "stress-timed," meaning that unstressed vowels (such as the "e" and the "o" in inverno) are often reduced, shortened, or nearly swallowed, creating a more "closed" sound.

Brazilian Portuguese Examples

1. Eu amo o inverno. (I love winter.)
2. O inverno aqui no Brasil é bem fresquinho. (Winter here in Brazil is quite cool.)
3. No inverno, eu gosto de tomar chocolate quente. (In winter, I like to drink hot chocolate.)
4. O inverno este ano está muito chuvoso. (Winter this year is very rainy.)
5. Eu preciso de um casaco para o inverno. (I need a jacket for the winter.)

Continental Portuguese Examples

1. Eu adoro o inverno. (I adore winter.)
2. O inverno aqui é bastante rigoroso. (Winter here is quite harsh.)
3. No inverno, gosto de beber chocolate quente. (In winter, I like to drink hot chocolate.)
4. O inverno este ano tem sido muito chuvoso. (Winter this year has been very rainy.)
5. Preciso de um sobretudo para o inverno. (I need an overcoat for the winter.)