Chris wrote

Do these appliances require any kind of provision to be
made for condensate drainage in normal operation?

Nope.

If not, how do they get rid of the frost?

It melts into a container above the compressor where
it evaporates using the heat from the compressor.

In very humid weather you sometimes hear a bit of
burbling when you close the door when the water
level in that container is higher than the end of the
pipe that puts the water into the container, but
the only time you ever see any on the floor is
when you move the fridge/freezer around and
tilt it too far so the container spills a little.