Do I get cold storage with my plan, or is that an extra I have to pay for?

It's included — that's one of the nicer things about the pricing. Paid plans come with a cold storage allowance bundled alongside your main "hot" storage at no extra cost. So on the 1 TB plan, for example, you're getting 1 TB of hot storage for active albums and 1 TB of cold storage for archives. Cold storage doesn't run the AI features, but for parking old albums and backing things up, it's genuinely useful and it's already in the price.