Not getting on you, but I was confused about the use of free reign or rein for a long time. When young I was told it referred to a riding method that allowed a horse to pick its own path. Looks like that may be correct...
“Free rein vs. free reign. The usual spelling of the phrase meaning freedom to do as one pleases is free rein, not free reign. The latter is a common misspelling, and it almost makes sense given reign‘s meaning (i.e., the exercise of sovereign power).”
Free rein vs. free reign - Grammarist
grammarist.com/spelling/free-rein-free-reign/
See also: give the horse its head