I want for products of a specific category to add an additional field with extra cost for packages, as shown here: http://i.imgur.com/bm9ccBC.jpg
Is there any mechanism in Magento by which to do this or require additional module?
You can use
Custom Options
in order to fulfill your requirement.
You can add this option from the Magento admin for a particular product. Please refer screen-shot.
The answer that Anx submitted is absolutely right. But you'll have to assign custom option to each product of that category. If you want to repeat the same custom option in multiple products, it will be a lot of manual work. The simplest solution to apply the same custom option to multiple products is through this free extension. http://www.magentocommerce.com/magento-connect/custom-option-manger.html
first, apply the custom option as mentioned by Anx, and then use this extension to copy paste it to multiple products. I used it on my site and it worked fine.