Has an NHL game ever ended 10-3?
It has. 10-3 has been a NHL final 39 times in 70,352 games. The first was Toronto St. Patricks beat Hamilton Tigers on January 26, 1921; the latest was Pittsburgh Penguins beat Philadelphia Flyers on April 18, 2012.
That makes 10-3 the 52nd most common final score out of 95 that have ever occurred in NHL. One point away, 11-3 has happened 21 times and 10-4 has happened 38 times.