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

Yes

The word "esquiar" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, vowels are generally more open and clearly articulated; therefore, the initial "e" in "esquiar" is pronounced distinctly. In Continental Portuguese, unstressed vowels are often reduced or almost swallowed; as a result, a Portuguese person might pronounce the word with a much shorter, more closed "e," making the "s" and "k" sounds transition more abruptly.

Brazilian Portuguese Examples

1. Eu adoro esquiar no inverno. (I love to ski in the winter.)
2. Nós vamos esquiar nas montanhas este ano. (We are going to ski in the mountains this year.)
3. Ela aprendeu a esquiar muito rápido. (She learned to ski very quickly.)
4. Você quer aprender a esquiar? (Do you want to learn how to ski?)
5. Eles estão treinando para esquiar profissionalmente. (They are training to ski professionally.)

Continental Portuguese Examples

1. Eu adoro esquiar no inverno. (I love to ski in the winter.)
2. Nós vamos esquiar nas montanhas este ano. (We are going to ski in the mountains this year.)
3. Ela aprendeu a esquiar muito depressa. (She learned to ski very quickly.)
4. Queres aprender a esquiar? (Do you want to learn how to ski?)
5. Eles estão a treinar para esquiar profissionalmente. (They are training to ski professionally.)