Harold wins at Hastings

Well, your work would consist of escorting your boss (the king or an earl) wherever he goes, and keeping an eye out for potential assassins. During times of war, you would have to fight in battle.

Other than that...

 

...and wear heavy chain mail while at work, and other weaponry, and a beard.

I guess most of the time the housecarls were doing other stuff, being part of the king's Gefolgschaft, favoured and rich.

 

No beard, never a beard.
Big mustaches were the English fashion in the 1060s, but beards? nope. Especially not on warriors - some unsporting chappie could pull it in battle, which would inconveniance you when trying to remove his head with an axe.

Other than that, yes, provided they kept themselves fit & trained, Housecarls were fairly rich, and relatively idle...

 

*sigh*

Historians are exhausting people...

 

We're just natural pedants!

 

Oooooooooo rich I could suffer a little discomfort to be rich. 8)