No you don't have to unlock the Big Park first. Festival Parks were added with Seasons. Your regular game towns automatically come with a Festival Park. They replace the original Big Parks. On Sims holidays festival items are added to the regular park features.
You should find the Festival Parks in your Library/Bin in the community lots section. Not sure of the wording but they will have and icon to match the EP their town comes in and possibly the name of the park. But they defiantly have "Festival Park" somewhere in the title of the lot.
Edit: Probably being to helpful, most people know this already. Hmmm.....I'll leave the post just in case another view helps to make a decision.