Are singers musicians?

The human voice is a musical instrument. Professional singers, particularly operatic, generally require extensive ongoing training in the use of their voice as a musical instrument.
If the definition of musician is one who uses or plays a musical instrument then singers are by definition musicians.

Absolutely yes.

That depends on your definition of musician. Loosely, anyone who makes music, vocal, percussion, or instrumental, is a musician.

If you hold the term musician to a higher standard, then only someone who is musically literate and has developed both the specialized knowledge and skills of music can be called a musician. Certainly, there are literate, skilled, and knowledgeable vocal musicians (Annie Lennox for example), but the average pop singer is not. And by this definition, the musicianship of many pop/rock instrumentalists could also be denied.

All singers and instrumentalists are musicians. Despite the fact that they are using their voice the singer must create and convey a musical idea. This idea might be a relatively simple pop song or a more complex one, like those typically found in jazz and opera. Interestingly, I can recall a conversation between Ella Fitzgerald and Andre Previn. Previn is one of the few musicians who can play jazz and classical music. At one point in their conversation Fitzgerald, being modest, stated that she wasn’t really a musician. Previn wisely disagreed with Fitzgerald’s assessment. I’m with Previn.

The American Heritage® Dictionary of the English Language: Fourth Edition. 2000, states that a musician is:

...One who composes, conducts, or performs music, especially instrumental music.

Therefore, in addition to instrumentalists and singers, both composers and conductors are also musicians.

Makes sense I guess!