I make a lot of cookies at Christmas, and I use good grocery store butter. Would anything change if I upgraded to European butter (which supposedly has more fat and less water) or cultured butter? These are american recipes, so I’m assuming they were tested with regular butter. Is the difference in fat and water enough to make a difference?
I make a lot of cookies and baked goods, and have never seen a problem with substituting European style butter into a recipe designed for American butter. I have seen a problem with the reverse - certain puff pastry and laminated dough truly are better with European butter, and switching to American butter has a negative impact on their texture.
I think you could probably safely swap European butter into any American cookie recipe.
That said, I wouldn't necessarily recommend it for all your Christmas baking. Like I said, I do a lot of baking, and European butter (at least where I live) is significantly more expensive. Any cookie where butter isn't the main flavor - chocolate crinkles, gingersnaps, nut-based cookies, etc. - isn't going to see as much benefit from European butter. I save my fancy butter for laminated doughs where texture is important and cookies like shortbreads where butter is the main flavor. I have to say, European butter makes absolutely the best shortbreads and sablés.