Did you read the DBI documentation for the do method? It clearly states:

This method is typically most useful for non-SELECT statements that either cannot be prepared in advance (due to a limitation of the driver) or do not need to be executed repeatedly. It should not be used for SELECT statements because it does not return a statement handle (so you can't fetch any data).

This is mostly a cut and paste from your code and has not been tested:

use warnings;
use DBI;
use DBD::mysql;
use CGI qw( :standard );
use CGI::Carp "fatalsToBrowser";
print header, start_html('SQL Must Work!');

my $dbh = DBI->connect("DBI:mysql:data:server","uname","pass") or
  die( "Could not make connection to database: $DBI::errstr" );

my $sth = $dbh->prepare( qq{SELECT Tab1, Tab2, Tab3
       FROM UData } ) or die $dbh->errstr;
my $rc = $sth->execute or die $sth->errstr;
if ($rc > 0) {
  while (my @row = $dbh->fetchrow_array ) {
    my ( $item0, $item1, $item2 ) = @row;
    if ($item0 >= $somevalue) {
      print br, "$item0";
    }
  }
} else {
  # check if there were no results or an error
}
$sth->finish;
$dbh->disconnect;
print '<h2>All Done</h2>';
print end_html;
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