Driveway Gutter / Rain Guide?
I'll let others chime in with gutter ideas.  Just keep in mind that you'll need to make sure they can handle the expansion from ice without cracking.  But I did want to mention a few alternative solutions you may want to consider.

If you want to keep the lawn, you may consider at a french drain, possibly with some ground level openings to handle severe weather (install these in a way that you can close them in the winter).

If you want to change the look, consider some raised beds on either side of the driveway (which has an added benefit of keeping cars off of the lawn).