Using slightly damp CLEAN wrung out scrims is an artform in itself...you can do it, but...er, why bother with all that effort??
An experienced window cleaner will only use a couple of scrims a day.
And with the advent of of microfibre cloths the scrim is almost redundant, they are the dogs whatsits
They work best when dry, but they are pretty cheap now, so have a few and rotate them regularly.
Ditto scrims to be honest.
I might be WFP now, but even in the most humid of conditions a half dozen scrims would last me all day.
One of the problems with using a damp scrim for polishing is that it has to be a very clean scrim, and it has to be barely damp for best effect.
As Dai said, you need to wash it out several times with clean, fresh water; soapy water isn't ideal as you have detergent residue impregnated in the scrim, with the result that the windows are not going to be as clean as you think they are.
I know this is a trad thread, and I'm not meaning to subvert it, but in the foggy conditions we have had just recently, or any weather condition with very high humidity...well, it just doesn't make a ha'peth of difference, it really is just bisiness as usual.
Ian