I was making pancakes that called for melted butter in the recipe and when I added cold milk the butter re-solidified. How did that mess up the pancakes? Was the texture more dense and less fluffy? So I presume this batter could not be made ahead of time and refrigerated?
The butter needs to be melted so it will emulsify with the eggs and milk. This makes a better pancake texture but your pancakes will still be recognizable and tasty if the butter did not fully emulsify.
As Max suggested in a comment, you can make your milk warmer. You can also make your butter warmer- short of burning it- to give yourself more time. You can replace some of the melted butter with oil.
Once the batter is assembled at room temperature there is less risk of the butter separating. Therefore, mixing the wet and dry ingredients before the butter can solidify is useful. In this case the flour would slightly warm the milk.
However you do it, making pancake batter ahead of time is generally a bad idea because the chemical leavening in the batter will activate and be expended. You might get a second lift from double acting baking powder but it still won't be as fluffy.