WooCommerce Tax Filter Not Working

You should get the subtotal like this:

global $woocommerce;
$cart_subtotal = $woocommerce->cart->get_cart_subtotal();

From here. So you will can do something like this:

add_filter( 'woocommerce_product_tax_class', 'big_apple_get_tax_class', 1, 2 );

function big_apple_get_tax_class( $tax_class, $product ) {
    global $woocommerce;
    $cart_subtotal = $woocommerce->cart->get_cart_subtotal();
    if ( $cart_subtotal <= 110 )
        $tax_class="Zero Rate";

    return $tax_class;
}