Horace was born in the Louvre, where his parents were living at the Revolutionary time. According to his father's sketchy Wikipedia entry, Horace's aunt was a victim of the Terror. However, the rest of the family avoided her fate despite their connections to the Ancien Régime. As for the adult Horace, he made sure to have ties to whatever régime was in power, be it Bourbon, Orléans or Bonaparte. Due to these connections as well as his talent, Vernet had a successful career in those pre-modernist times.
His subject matter was military scenes, Orientalism and portraits. Examples are below.
An indication of regard for Vernet.
An early work painted the year of Napoleon's return and Waterloo.
Painted the year after Napoleon's death on St. Helena.
Vernet painted several scenes of Napoleon's battles.
Olympe Pélissier (1799-1878) had an interesting life, as this link indicates.
The French Foreign Legion during the conquest of Algeria.
Note his North African garb here an in the statue in the first image.