Can a value be moved by taking a mutable reference?

Playpen

pub trait Skip<I: Iterator> {
    fn skip(&mut self, steps: usize);
}

impl<I: Iterator> Skip<I> for I {
    fn skip(&mut self, mut steps: usize) {
        for _ in self {
            steps -= 1;
            if steps <= 0 {
                break;
            }
        }
    }
}

fn main() {
    let s  = "abc123def";
    let mut chars = s.chars();
    chars.skip(2);
    println!("{:?}", chars.collect::<String>());
}

Error:

error: use of moved value: `chars` [--explain E0382]
  --> <anon>:20:22
19 |>     chars.skip(2);
   |>     ----- value moved here
20 |>     println!("{:?}", chars.collect::<String>());
   |>                      ^^^^^ value used here after move
<anon>:20:22: 20:27: note: in this expansion of format_args!
<anon>:20:22: 20:27: note: in this expansion of print! (defined in <std macros>)
<anon>:20:22: 20:27: note: in this expansion of println! (defined in <std macros>)
note: move occurs because `chars` has type `std::str::Chars<'_>`, which does not implement the `Copy` trait

error: aborting due to previous error
playpen: application terminated with error code 101