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The cedar railings actually look fine. They used a different color and
paint for the "deck" deck -- that is the part of the deck you walk on.

The deck has gotten little, if any use since they painted. Indeed, no
one used it for three full weeks after painting, as the house was
vacant.

Anyway, the winter rains came and all the paint on the walking part of
the deck is peeling and coming up in big strips. It will continue to
be damp and rainy here for three or so more months, but is there any
special way I can clean up this mess now?

Very common on decks. It get beat up by the weather and because of the
grain in the wood, it is easy for moisture to get under it. Hopefully, they
used stain, not paint. This is why decks are best left natural.