Freezing depends on what you're freezing and how long you freeze it! You very well could get rid of it the first time. I know a person who visits a dermatologist twice a year just to have about a dozen moles removed at each appointment (some people have a lot of them and don't want them, etc.)

Many years ago, I had a Planters wart on the bottom of my foot and it only took 2 applications of liquid nitrogen to freeze it off and I think it was deeper than most moles.

(moley, moley, moley- OK, I couldn't resist). If you have no clue what that was about, watch the Austin Powers clip below:
oh, I totally got that reference. i'm a bit of an austin powers afficianado.
We'll see. It's a small mole, about the size of half a pencil eraser.
Take care,
brett