I walked into my workshop one day after a thunderstorm and found the FM radio wouldn't work. I opened it and found capacitors in the tuner blown apart , pesumably by a lightning strike in vicinity of my outdoor antenna.
Next day i noticed two magnetic compasses i keep near workbench pointed South instead of North. I called Silva and spoke with their engineer, he said to send them back for remagnetization.
I did it myself with a soldering gun. Found it quite easy.
So part of your answer is "Yes it can be done"
but i have no idea as to field strength required.
For fun, take a soldering gun and hacksaw blade and feel how strong it vibrates when held near the high current heating element. You could measure flux with an open coil and calculate a ballpark answer i think. That'd give a number for the iron in compass needles, at least.
just an approach .