I am not aware of any such setting for Cells, and I didn't find anything in the options inspector. But I also may be misunderstanding. How would you edit a cell that only showed the first line (assuming there was stuff in the cell below the fold)? Do you want to be folding/unfolding every time you edit? How should the width of the notebook influence what shows in a folded cell? Is there actually some further objective that you're trying to achieve that you haven't told us about?
Like maybe you want to know where a symbol is defined but you want to hide the definition. You could do this by putting a text cell just before the input cell where the definition is. The text cell could contain the symbol name and you could hide (close) the input cell. Or, better yet, use a cell type that has grouping rules (e.g. Section) instead of a text cell. Then, instead of hiding the input cell, you could just close the group.