The MP is a function of the RPM, throttle position, and delivery pressure to the carb
And, density of the air going into the carb. Heating the air, will reduce its density.
The "pressure" of air going into the carb of a normally aspirated engine will be atmospheric plus a very minor ram pressure which will be a factor of airspeed. The maximum ram pressure which one could expect in the speed range of a Cessna 182 would be just under 1 inch of mercury, low airspeed to fast airspeed. Detectable on the MP gauge, yes, though probably less effect than the changed density of the carb heat hot heated air if selected.
If the induction air filter becomes suddenly blocked in flight - freezing rain on the filter (and windshield!), which I have encountered, MP will suddenly drop, just as closing the throttle the engine can't get enough air to run at high power. Selection of carb heat is also alternate air. This will bypass that blockage, and return you to maximum power, less the effect of the less dense hot air. If you have selected carb heat hot, then cold again, and had a net increase of MP, you had carb ice, and melted it away. The RPM remained the same the whole time, as the propeller governed as intended. On a fuel injected engine, there is no carb heat control. There may be an alternate air control, which if used, should have no effect on MP, as the alternate air would be the same density, just a different source. Some fuel injected engine installations have no alternate air control, the alternate air door in the induction system is automatic (held closed by a spring and/or magnet).
If you change the RPM by moving the propeller control, the MP will increase with RPM decrease, as with the increased blade angle of lower RPM, the engine has to produce more power to turn the more coarse prop.
As I took off once in my 150 on a damp day, I suspected carb ice, so I selected carb heat hot. The engine quit a moment later, and I conducted an EFATO forced landing, which was a success. When I stopped rolling, the engine was running at a stumbling idle, but would not respond to throttle movement at all. I towed the plane back to the hangar and took the cowls off to investigate. There was gasoline soaked fiberglass insulation wadded up in the throat of the carb. Mice had made a nest in a hot air hose, from insulation pulled from under the glareshield. They did it fast, as I'd flow he plane a few days earlier with no problem. I cleaned out the fiberglass from the carb, and the engine ran fine. I made a screen in the hot air hose elbow to prevent a future occurrence, and have not had a problem since. The wadded insulation acted like a close throttle, and changed the engine power to less than idle. Obviously, this was downstream of the the alternate air, so that would not help the situation. Now I do not select carb heat until I'm well up in other planes I fly, just in case!