Did "Karolus Magnus" (Charlemagne) ever cross the Alps on horseback as the painter Louis David seems to suggest in his famous painting of Napoleon doing so?

According to H E Marshall's "The Story of Europe" -
"So across the Alps Charlemagne passed with a mighty army." (my edition is published by 'Yesterday's Classics' and the passage is on page 53)
This was in response to the Pope Adrian I asking for his help to subdue the Lombards.
As Charlemagne was the leader, and in his prime, it is likely that he had the finest horse money could buy, to ride as he led his troops to battle.

OK, thanks. That solves the problem.
This is a picture of the painting.
https://en.wikipedia.org/wiki/Image:Napoleon4.jpg
Image:Napoleon4.jpg - Wikipedia, the free encyclopedia