Replacing glass in antique 3 panel 2 light doors?

I have some doors that are "5 panel" - 4 verticle panels and one horizontal panel - except the top two verticle panels are glass. I've seen this referred to as "3 panel 2 light" doors.

Anyhow, I'd like to remove the 2 "lights," and the wood between them, and replace this with one large window. How exactly is the existing glass held in? Is the coping I'm looking at just trim nailed on the keep the glass in place? There's so much paint I can't tell. And then, how do I get the verticle piece in the middle out? Just cut it horizontally in half, then try to pull it from the horizontal pieces it buts into?
thanks!