With UI, whenever you create any CloudFront distribution, open that distribution.

1. At the right, you will find Logging tab >> Add
2. Select S3 in Deliver To option
3. Destination S3 bucket
4. Now, you there will additional-settings section (optional). It will have field selection. Here, you can select Coookie field among all other fields like x-forwarded-for, date, time.

With IAC, Are you following example from latest version? https://registry.terraform.io/providers/hashicorp/aws/latest/docs