python Guess The Number
Positives

Your function docstring was informative and helped me understand the code better.
Good use of variables like cursor_up to manage the ANSI control characters

Small improvements

As long as you're bringin in colorama, can you use any of the named constants in provides instead of the control characters?
If you need to do something multiple times, I like to see if there's a good way to do n times instead. See if you can make the number of turns more configurable.
I'm not sure what you're doing with line = cursor_up_ask + answer_sz + cursor_up. This would be a good place for a comment or a function with a clear name.
You're taking len(answer), but shouldn't that always be 1? My understanding is that you're expecting a one-digit answer. It would be nice to have some error handling so that, e.g. 23 isn't treated as a valid guess.
You could eliminate the pool global by wrapping it and your functions together in a class. You could also eliminate the global by having more focused functions.
Instead of doing a find-replace on the * in MSG_TRY, you can do something like this:

MSG_TRY = '\033[91mTry again {}\033[0m'
msg_wrong = msg_wrong.format(hint)

Larger gripes

I'm finding the flow of the program hard to follow. Consider breaking it down into smaller functions so it's more clear what's going on. It could look something like:

def play_one_turn(final_turn = False):
    guess = get_player_input()
    if guess == right_answer:
        print(OK_MSG)
        return True
    if not final_turn:
        show_hint(guess)
    else:
        print(MSG_ANS)

(I'm not saying this is the best way to do things. It's showing how smaller well-named functions can give more clarity with the same structure)

exit() in the middle of a function is suspicious. (Is the code missing from sys import exit?) I'd expect to see it at the end of a main function to return a status code back to the user. It should not be used for control flow. It would make more sense to return True or False depending on whether the guess is correct, and let the caller manage things from there.