Hides the product price on the frontend if it's set to zero in WooCommerce.

hide-zero-product-prices.php

/**
 * Hide price if it's set to zero
 */
function a8c_hide_zero_prices( $price, $product ) {
	if ( '' === $product->get_price() || 0 == $product->get_price() ) {
		$price = '';
	}
	return $price;
}
add_filter( 'woocommerce_get_price_html', 'a8c_hide_zero_prices', 10, 2 );

/**
 * Hide the Add to Cart button for products with zero price
 */
function a8c_hide_add_to_cart_zero_price( $purchasable, $product ) {
     if ( '' === $product->get_price() || 0 == $product->get_price() ) {
          return false;
     }
     return $purchasable;
}
add_filter( 'woocommerce_is_purchasable', 'a8c_hide_add_to_cart_zero_price', 10, 2 );