HDP is hundred percent open source platform that your client can install and start using. While your client can use the software for free, they will get no support if they run into any issues. Remember, every software when implemented in large scale production, runs into issues. Your client will be on their own if they don't buy Hortonworks support. So, short answer: Software is free and your client can go ahead and use it without any legal repercussions. However, to reduce risk to business, your client is better advised to buy support from Hortonworks.
In addition to @mqureshi update. You can get more detailed information about the paid services and subscription from the following links:
2. HDP / HDF subscription and support overview: https://hortonworks.com/services/support/enterprise/