Do this:
(defvar my-hist nil)
(make-variable-buffer-local 'my-hist)
(defun my-function (hist)
(read-from-minibuffer "> " nil nil nil hist))
(defun my-command ()
(interactive)
(add-to-history 'my-hist (my-function 'my-hist)))
Don't quote hist when you pass it to read-from-minibuffer. You want to pass its value, e.g. the symbol my-hist, and not the result of evaluating 'hist, which is the symbol hist.