Here's 58 chars with a completely different approach. .
`sub f{($s,$t)=@_;$$t{d}eq$s?$t:f($s,$$t{l})||f($s,$$t{r})}`
--twerq | [reply] [d/l] |

As koolade pointed out, not all of these
work. Yours in particular goes into deep recursion.
Works in theory is not good enough, in golf you are going
to learn a lot about the assumptions you cannot make.
And yours has at least 2 separate (and serious) mistakes.
BTW the counts as I list them are just for the body of the
sub, so if yours did work it would be 51 characters.
Playing independently I came in with several solutions
that are small, and the following which is similar to
yours really does work at 58:
`sub f {
my($s,$t)=@_;$t?$$t{d}eq$s?$t:f($s,$$t{l})||f($s,$$t{r}):0
}
`
And here, thanks to koolade, is the test that I use:
`$t = {
d => 'd',
l => {
d => 'b',
l => { d => 'a', l => 0, r => 0, },
r => { d => 'c', l => 0, r => 0, },
},
r => {
d => 'f',
l => { d => 'e', l => 0, r => 0, },
r => { d => 'g', l => 0, r => 0, },
}
};
sub test {
my $val = f(@_);
print $val ? "$val->{d}:$val\n" : "$val\n";
}
test('e',$t);
test('O',$t);
`
| [reply] [d/l] [select] |

Both tilly and indigo have exactly the same result,
which is a fix of twerq's including 1) my, and 2) the
test for $t which prevents infinite looping.
Here is a solution which is short, but not 'strict' compliant:
`sub f{for(($s,$t)=@_;$_=$$t{(0,l,r)[$$t{d}cmp$s]};$t=$_){}$t}`
Alas, although 4 characters lighter, it doesn't return 0 on misses properly. This does,
but is admittedly 3 characters heavy:
`sub f{for(($s,$t)=@_;$_=$t&&(0,l,r)[$$t{d}cmp$s];){$t=$$t{$_}||0}$t}`
Or, a tie, provided the tree has 0-value stubs as it does in
other examples:
`sub f{for(($s,$t)=@_;$_=$t&&(0,l,r)[$$t{d}cmp$s];){$t=$$t{$_}}$t}`
Fun test code below for a tree:
` $|++;
$table = {
d => 'h',
l => {
d => 'd',
l => { d => 'b', l => { d => 'a' }, r => { d => 'c' } },
r => { d => 'f', l => { d => 'e' }, r => { d => 'g' } },
},
r => {
d => 'l',
l => { d => 'j', l => { d => 'i' }, r => { d => 'k' } },
r => { d => 'm', l => { d => 'l' }, r => { d => 'n' } },
}
};
foreach $y (qw[ a b c d e f g h i j k l m n o p q ])
{
$x = f($y,$table);
print "Answer for $y = ";
print $x," ", $$x{d},"\n";
}
`
value entry in the hash. | [reply] [d/l] [select] |

Comment onRe: Golf: Tree searchingSelectorDownloadCode