The issue with humidity and condensation on tools is simple, as you heat your work area (particularly if you let it get near freezing or below) for a longer period the metal cold soaks. What happens as you heat the shop the relative humidity changes (temperature dependent) except at the surface of the machine as it near freezing. What happens next can best be described as your heavy metal machine becomes the shop dehumidifier by pulling any and all moisture out of the air and condensing it (unfortunately) on its surface. Over all this is not the extra moisture from unknown sources, but by letting the machines cold soak and then heating the shop when we need it we create a clone of the dehumidifier.
To be fair different heating methods can cause issues, but overall if cold soak can be avoided, condensation can mostly be avoided, again unfortunately some shops can not do this so other preventative measures need to be taken
That is mostly a wives tale. The science says it doesn't happen that way. To do that, the air next to the machine would have to increase its moisture by attracting moisture from elsewhere.
Looking at it a different way, the air right next to the machine doesn't know the heater has come on. It wasn't below the dew point beforehand, and there is nothing to make it colder because it's already as cold as the machine. So it can only reduce its humidity as it warms. Even if it never warms, that little piece of air can never get to a higher water content than it had when it started. Unless more water is added.....
Similarly, other units of air elsewhere in the room are warming, but their water content is not changing either (unless water is added) so their humidity level is diving. Even if air currents take them back to the machine where they cool, their water content does not change. Therefore they cool but never colder than the machine which was a temperature above their dew point.
Most of the wives tales on this matter are the result of higher daytime humidity from lots of sources including humans, overnight cooling below the dew point, and water that condensed when the dew point was reached during the night but not noticed until after the heat comes up a bit.
Another source for the wives tales is the result of excess water someplace (ice, frost, puddles, leaks, people breathing on things, drips, sweaty concrete, wet towels, etc etc) that increase the relative humidity faster than the heater can compensate.
The third source of the wives tales happens with a well sealed cold room that is filled with cold air slightly above the dew point with cold machines and equipment in it. If the doors are opened and a rush of warmer more humid air enters the room (from outside or from inside the house), that warmer air mixes rather quickly with the rest of the room air significantly raising the average overall humidity. Because it usually does have way more moisture in it, that excess water can condense when it encounters the cold machine. Not only that but because warm air holds so much more water than cold air, it doesn't take much cooling from those giant heat sinks to condense that water back out of the air. Here is a rather interesting corrolary of that science. If you mix equal parts of air with one part at 30 degrees F and 50% humidity and the other part at 50 degrees F and also at 50 % humidity, the result is air that will be 40 degrees F, but much higher humidity. Prolly 70 % or so. You can do the exact calc using a psychometric chart if you want by obtaining the pounds of water for both samples and then looking up the humidity using that new total mass. If both parts were at 100%, guess what happens? Yup, lots and lots of dew! This is the outcome of that non-linear relationship I described earlier.
In summary, there is no science to support what you think is happening. Nonetheless, what you saw did happen. You just need to figure out why/how it happened. Hence my desire to help you find it. You cannot fix a problem if you don't know why you have it.
If that doesn't make sense, I'd be happy to try and explain the nuances further and/or explore other explanations with you that you might suggest. Might be better in a phone call to avoid boring other members to death though. Or better yet over a few beers to improve the efficiency of the discussion... LOL!
Edit - here is an experiment you can try. Next time it gets cold in your shop, take a big block of cold steel from your shop, put it in a big zip-lock bag, and then bring it inside the house. No dew will form on it. Do the same thing with another one but leave the bag open. It may or may not end up with condensation on it depending entirely on the humidity level in the house.