Refer to figure.
In a piston engine, the mixture ratio is the ratio between the mass of fuel and mass of air entering the cylinder (NOT volume). The mixture is controlled by adjusting the fuel flow only, as for standard reciprocating engines (with no turbo/supercharger) the air entering the cylinders cannot be directly controlled. This is why in order to maintain a constant air/fuel ratio with increasing altitude, the fuel flow will be reduced. This will compensate for the decreasing air density with increasing altitude.
You always need to climb with a fully rich mixture because this will provide you adequate cooling and will lower the cylinder head temperature. In fact, since the forward speed of the airplane is not high enough to collect enough air for engine cooling, the extra (unburnt) fuel will be the main cooling element during climb segments.