Title also takes in our Moon and Phobos and Deimos.
One may as well throw in Ceres as well, and it wouldn't matter if Mercury were included. None of these have any atmosphere to speak of, and therefore no weather to control.
The art of weather control as I see it is to perceive weather as a heat engine, and simply control the heat that enters the system in order to control what it does once there.
Mirrors are the key to this: An extremely large mirror in the Earth-sun LaGrange Point One, to deflect incident solar radiation from Earth's equatorial regions, and to redirect it toward the poles as needed to move things around. Essentially one guides the trade winds in their courses to keep them predictable.
For Mars, of course, the situation is different; one needs to add energy, and a lot of it. Mars is twice as far from the sun as Earth, on average, and receives only a fourth of the sunlight that Earth does. To make it more like Earth, we need to put a big, (yes, that big), mirror in its Mars-Sun LaGrange Point One, so that the nearly twenty-four hour day of Mars is preserved, but with considerably more heat and light.
A resident of Mars, looking up, would then see a sun as large to the eye as it appears from Earth, and therefore plants adapted to Earth's light levels would thrive there, assuming they had air.
This additional heat on Mars will release both water and carbon dioxide to replenish the Martian atmosphere, but more air from someplace will be needed. Mars is a fixer-upper, but the weather system will be easy.