Games in the rain?

[Nathan Ross]

There's a note in Suetonius Domitian (4,2): "He often gave sea-fights almost with regular fleets, having dug a pool near the Tiber and surrounded it with seats, and he continued to witness the contests amid heavy rains."

This implies that watching games in bad weather was not usual. I would think that it was more of a problem of the spectators getting soaked than the fighters (especially in a 'sea-fight'). Presumably if the emperor insisted on sitting it out then everyone else had to do the same...