My bet is the battery. You can get it load tested. Yes, the headlights will glow but not have enough juice to start it.
Is this the original battery? If so, consider yourself lucky and enjoy the investment of a new battery.
Be advised that a lot of companies list batteries for your car. It is not only the electrical specs, but also very specific physical specs. There are some VERY nasty automotive stories about batteries being installed, especially in under-seat locations where they had the right cranking amp hours, fit length and width, and shorted out because they were too tall contacting the seat springs.
Winters are hard on batteries: cold thick oil, short trips, rear window defoggers etc.
Just be sure, thats all.
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)