Refactoring is good. Refactoring without testing is nearly impossible.
That's a bit strong. While cleaning up or migrating legacy code, I've done a lot of refactoring without having a solid base of unit tests. It can be done, but it's tough on the psyche.
I think a more accurate statement is:
It is difficult to refactor with confidence without having a complete set of regressions tests that cover the code you're refactoring.
In fact, having adopted the "write your tests first" dictum from eXtreme Programming, I'm finding it uncomfortable to do any
development without having a set of regression tests at hand. An infectious notion, that.