Yes, governments should be permitted to micro-engineer their climates if it helps the environment. So long as micro-engineering the climate of the country does not affect the climate of another country or negatively affect the environment, countries should be allowed to enhance their climate with technology to improve living conditions in the country.
No, I do not believe that governments should be permitted to micro-engineer their climates. We are not God, and we can mess up a whole lot of other things by trying to engineer a micro-climate. Sensible regulations are fine, but no government should have the power to completely engineer a micro-climate.
The United Arab Emirates are seriously considering building a mountain in order to offset the massive amounts of heat that they are suffering under climate change. However, this mountain would cause enough harm to outweigh any potential benefits: this micro-engineering plan might affect their geology - or inadvertently affect the climates of their neighboring regions.
Many amazing technologies exist in this world that are in our society's hands. That does not mean that we should mess with them. The climate--the weather--is God's work. The sun shines and the raindrop falls just the way he wants them to. Every state and country's weather is perfect according to his plan.