Like A knack for horses mentioned, you aren't able to remove a thread or post yourself but can edit them within the next 10 minutes after sending the post.
If you want to delete a thread, you have to contact the Horseforum upkeeping Team. You can contact us via 'Talk to the Team' sub-forum or sending a private message to the Administrator or some of our moderators (moderator users have this golden star icon above their avatar picture).
In most of cases, we don't delete posts or threads just by a request since for example removing posts from some discussions would make the thread and the forum hard to read and understand. The most common reason we remove or edit something is that the thread or message contains personal information or violates Horseforum.com rules.
Anyways, if you've any concerns related to this or anything else, please feel free to contact the Team using 'Talk to the Team' subforum or sendind a private message