Historically animals like deer kept meadows open.

Yes, a dense forest is not always good for the native species. Deer or bears, for instance, need these small deforested pockets to survive. I think that was one of the problems of preventing all forest fires. Now, in certain places, there are controlled fires to clear certain parts of forests.

I don't have figures but I guess growing forest are mainly replacing perpetual meadow

That's actually the standard model, at least when I took ecology: there's actually a whole biome described as the "woody invaders". I've never heard of woody retreaters, or grassy invaders.