I messed up with my first account, which is this one. Is it okay for me to make a new account, transfer my favorite horses to the new one, then terminate this one?

No. Transferring anything between accounts is cheating. You are free to create a new account though. You are allowed a max of 3 free accounts per household. Accounts are deleted after a period of time by not logging in (3 months for a free account).

Okay, thank you. I did not want to break the rules, and now I understand. So all I have to do to delete an account is not log in for 3 months?

Yep, exactly.