Would removing window posts damage structural integrity?

The load above the window is supported by a header, usually made of double 2x12s which span from one side of the window to another. Your posts may sit under that. If so, it may be possible to remove the posts if the span is not too long. They could also be framed with a header spanning from post to post and supported at each post. If that's the case, they cannot be removed withou destroying the structural integrity of the wall. Hope this helps. Good luck.

The only way to know for sure is to remove the sheetrock above the window to exspose the header beam and see if it spans the entire opening. If it does not, (which I highly doubt) you would have to remove it anyway to install one. (That is if you still plan on removing the posts).

For individual headers to be put in during construcion, you would need a minimum of four 2X4s between the windows to allow for the proper header supports. That would be a minimum of 6 inches of wood. If your posts are not 6 inches wide, it would be highly unlikely that they are main supports.

Please note that the manner in which you want to reframe the windows requires a building code check and review by your local building and safety department.