That said, are there any advantages to tricycles (for people who can ride a bicycle)? Riding on ice, perhaps?
Not really. [...]
Recumbent trikes, on the other hand, are a completely different class of beasts: Steering tends to be vastly more intuitive for a bicyclist (although unlike a bicycle you still have to think about camber), stability (and associated 'fun') varies according to the geometry but is generally far better than upright trikes as the centre of mass is lower, and wind resistance can compare favourably to a DF bike. The above points about weight and rolling resistance still apply, and traction can sometimes be interesting.
The one thing that trikes (of all kinds) are *really* good at is going slowly. Hence the popularity of tadpole 'bents with really wide gear range as touring machines.
Every bicyclist should try to ride an upright tricycle at least once. It'll teach you more about how a bicycle works in the time it takes you to crash into the kerb than a lifetime of bicycle riding...