Yes, the Roman holiday of Saturnalia was a feasting period during which slaves and masters swapped some social norms. For example some literature indicates that slaves might have eaten before their masters during Saturnalia, and slaves and citizens would both wear a hat that usually designated one as a freeman.
Saturnalia is marked by
Saturnalia also had parallels, possibly influence, with the late Medieval Feast of Fools as well. During the Feast of Fools roles would again be parodied.
I don't watch Downton Abbey so I can't say whether they're referring to Saturnalia, the Feast of Fools, or another similar holiday but they are variants of a similar theme.
In the British Army, it is traditional for the officers to wake the enlisted with Gunfire (tea, laced with rum), and then, operations permitting, they will go on stag, which means they'll do sentry duty, radio watch etc, for a portion of the day. Cordingly's book on the 1991 war indicates the officers covered the duties until noon. Both the British and US Armies traditionally see officers serving the enlisted their food on Christmas. I must admit to having been unaware of s civilian equivalent.