According to Chapter 5 of Freakonomics, does exposing children to art museums or to classical music help them become more intelligent/successful?

The short answer to this is "no."  The authors find that
there is no correlation between this sort of thing and a child's academic ability later
in life.

Towards the end of Chapter 5, the authors present
a list of things that do and do not correlate with higher test scores.  One of the items
on the list of things that do not correlate is "The child's parents regularly take him
to museums."  (This is on pp. 174-5 in at least one edition of the
book.)

The point of this chapter is that the things that
parents do are less important than the things that they
are.  In other words, activities and such things are much
less important than demographic factors.  What matters is whether the child's mother is
above 30 years of age when the child is born or that the child's parents are highly
educated.  These things are more important than whether the child watches TV a lot or
whether the parents read to the child often.

Therefore, the
answer is no.  Things like "Baby Mozart" or going to museums are not likely to improve a
child's intelligence or likelihood of success.