The NASA video Juno Engineering: Precision Matters shows the Juno spacecraft on what look like it might be a spin balance table after about 02:50
and there one can see that much of the whole spacecraft is wrapped in a dull, reflective film.
According to @Dave's excellent answer the dish is covered not with aluminized or metallized foil, but with a germanium coated polymer film. The semiconductor is thin enough and has such a low carrier density that it is fairly transparent to microwaves and yet because it has an optical band-gap, still opaque to the Suns light (physics discussed more in this answer). This provides some thermal stabilization against temperature changes caused by sunlight.
Juno has several Microwave Radiometer antenna arrays on it's sides as well, and those also appear to be covered with the same germanium foil.
As far as I can tell many if not most recent deep-space spacecraft have their dishes and possibly other antennas covered.
But I don't think the early ones did. As far as I know the Voyagers' dishes were completely open, and I think (but I'm not sure) that Cassini's was open to space as well.
Question: When did deep-space probes start getting covered in germanium-coated films? Which one was first?
Here's a photo of TESS, used in The appearance of TESS' dish seems to be evolving, what will be the final configuration? sourced from Solar Panels Opened on NASA’s TESS Satellite. Photo credit: NASA/Leif Heimbold