What kind of fermenter are you talking about? I hope it's not a carboy!
I would bring it in rather than let it freeze, if the garage will stay even a little warmer it might not freeze at all depending on how strong it is and how long the temperature takes to drop. Although at 22F, overnight night not be long enough for it to freeze solid.
For what it's worth, a 10% ABV solution will freeze at 25F - it's not quite linear, but it gets you in the ballpark. The other things in the beer (residual sugar, proteins, etc) will also alter the freezing point somewhat.