All treatments are most effective when there is not brood.
But OA trickling is the only method which you can use in middle of winter.
Oxalic acid will kill off many probiotic microbes
The real question is how many are on the bottom board and over how long a period. Slip a sticky board in for 48 hours and see what you get.
This idea I have not seen for many years. It has nothing to do with bees' wellfare.
I have now here -15C frost and next night -24C. It is better that probitotic creatures find a better place to live.