They are splined on the motor side of the wiper. In some cases you can press the wiper arm back on there and tighten the nut down and be good to go. Last winter my passenger side wiper let go, I pulled the arm off, cleaned everything up and tightened it back down and its been good to go ever since. Of course I havent tried to move all the ice out of the way that I did that day either.
Now, if the splines on the motor side are ruined that may be a different story. But if the splines are good there then you can either get a new arm and press it on there or try your luck in putting the old one back on and see if it will hold.
