Get Custom Attribute Value Without Loading the Product

Take a look at Magento change product name adding to cart

Use event sales_quote_item_set_product

class Mynamespace_Samples_Model_Observer
{
    public function salesQuoteItemSetProduct(Varien_Event_Observer $observer)
    {
        /* @var $item Mage_Sales_Model_Quote_Item */
        $item = $observer->getQuoteItem();

        //only change the item you want by product id
        if($item->getProductId() == xyz){
            $item->setName('Ians custom product name');
        }

        return $this;
    }
}

If you are listening on checkout_cart_add_product_complete you have the following items on the $observer

 ['product' => $product, 'request' => $this->getRequest(), 'response' => $this->getResponse()]

Your code should look smth like this

$product = $observer->getProduct(); // or $observer->getData('product');
$customAttribute = $product->getCustomAttribute('custom_attribute_code');
// to avoid errors double check that this product 
// has the custom attribute associated to it
$value = $customAttribute !== null ? $customAttribute->getValue() : null;

It's also a good practice to use the debugger to see what is what and what properties and values are available on a given object.

Hope this helps. Cheers.

EDIT as result of the comment

You do not have the product loaded at that point. You only have the controller instance and the request as it can be seen \Magento\Framework\App\Action\Action::dispatch(). You must have smth on the request like a product_id or product_sku.

In a development environment if you don't have xdebug(you should really take care of that, it pays off) the fastest way to debug stuff is var_dump($object->getData()).

On this specific event what you can do is inject the product repository in the constructor, get the product id from the request and load the product.

smth like

$product = $this->productRepository->getById($observer->getRequest()->getProductId())

Once you have the product above should apply. You can add some extra checks like, is there a request on the observer data? is there a product id on the request and so on.