I just pulled the fork from my old Peugeot, and I've discovered why the bike was always pulling to one side the last few years: the fork is misaligned to one side. The centerline of the wheel is offset about 1/4" off the centerline of the steer tube.

I assume it's safe to cold set back to where it belongs, as it's a steel fork. Is that correct?

As long as there are no kinks and you don't put any in it you will be fine. Steel is easy to work with.