Correct, Al; as you climb, you must lean the mixture- because the air is less dense the higher you go, and this has the effect of making the mixture too rich. This is bad for fuel economy, and can foul the plugs. We can't just pull over if the motor fouls out. You can aim for 700 degrees CHT (or whatever temp is specified in the POH), but many small planes don't have this gauge, so you go by the tachometer- leaning for max rpm, then 1/2 to 3/4 turn richer.
Enriching the mix a little will cool a slightly overheated engine; for example, after flying a bit near stall (slow flight).
And yes, every plane with a carburetor and a gas piston engine still has a mixture control in the cockpit. It has a red knob, so you don't confuse it with the propeller pitch control, which is blue. They can be pushed and pulled, or turned for a fine control, and when pulled all the way out cut the fuel off completely.