We did it like you are describing as well. In fact I recall the first time I actually saw a grid, and I thought it was a wargame, and it looked like too much work compared to how we just used an undefined space on a table and moved stuff around just to represent vague positioning. It was not until 3e that I finally used a grid and found reasons to like it.
I remember playing AD&D 2e and we just scribbled on a piece of paper, it did work, although it could be a bit confusing at times. I really wonder if I can go back to playing more like that again. I think it will be pretty hard, since it's pretty ingrained to use the grid and count squares.