The opening is an element in the facade to balance the front entry. If I had to fill it in, I would would frame a new wall at the back and stucco it to create a recess where the opening is currently (IE not changing or removing the arch), then get a custom iron gate made that can act as a trellis. Or just get a wood door made for there that is never opened...

Very helpful, thank you. we are struggling to preserve the look of the original. The previous owners added a 3 car garage to the left of this door. The space was originally a patio, but it became an entry way to the house from the garage. There were originally 3 small windows to the room on the right, we are going to be adding 2 more to create 5 across (hence the sheathing). Otherwise, there are no changes to the outside of the house.

I would have a door made to replicate the one for the main entrance. There's good reason to be able to enter a mudroom from the front of the house as well as from the garage. I don't see anything else to do. I have a tudor from 1928, but it is not as grand as this.

Prop up some foamcore at the same height as the new/old windows next to the doorway. See if it looks pretty good or out of balance. If it's pretty good, get a window made to fit in the same style as the other new/old windows going in. If it doesn't work, have it all filled in and re-stuccoed to match. Add a shrub in front and it will look original to the house.