When I add this:

use Data::Printer;
p $data;
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I get this out:

\ {
    node   [
        [0] {
            name   "1st node",
            text   "Text of 1st node"
        },
        [1] {
            name   "2nd node",
            text   "Text of 2nd node"
        },
        [2] {
            name   "3rd node",
            text   "Text of 3rd node"
        }
    ]
}
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There is no key called 'App', so your @{$data->{App}{node}} is an empty list.

If I change your for loop to this:

foreach my $node (@{$data->{node}}) {
    print $node->{name}.": ".$node->{text}."\n";
}
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I get what you were expecting:

1st node: Text of 1st node
2nd node: Text of 2nd node
3rd node: Text of 3rd node
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If you want to keep the root key, you can use the following and keep your original loop.

my $xml = XML::Simple->new( KeyAttr => 1, ForceArray => 0, KeepRoot =>
+ 1 );
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