If the whole space is uninsulated, then the whole space may get cold enough to freeze the pipe. Just insulating right next to the pipe will probably not be enough in that case. Likewise, insulating the pipe itself probably won't help either if the cold conditions stay for long enough. A pipe heating coil/wrap/tape/element might be the way to go. Just a trickle of electricity to keep the pipe above freezing temperatures.

That said, adding insulation to the entire space will help, but that's a whole project.