BTR is probably not a true story. Usually, such works are the product of an author's imagination, designed to take us on an interesting and fictional journey.
In most cases, BTR is not rooted in a true story. It's more likely to be the product of the creator's imagination or a fictional concept developed for entertainment purposes.
Another option is Wattpad. There are many users on Wattpad who write fanfics. You might need to do a bit more searching compared to the other two sites, but you can often find some hidden gems. Look for groups or communities on Wattpad that are dedicated to BTR or 1D and see if they have any recommended fanfics that combine the two.
One great btr and 1d fanfic could be one where the characters from both groups meet at a music festival. They start collaborating on a song, and through that process, they become good friends. It's a really fun concept as it combines the charm of both Big Time Rush and One Direction.
I'm not entirely sure which specific 'Christmas BTR story' about Snoop Dogg you're referring to. There could be various tales related to his Christmas experiences or perhaps something related to a 'BTR' (not sure if it's a project, place or something else) during the Christmas time. Maybe it's a limited - edition Christmas album or event he was part of that's not widely known by this name.