It's a fair question especially because it's often argued by people who question the science and think the government is behind global warming. There's not much evidence behind it.
First, we need to define what government power really is, because it's a phrase that is thrown around like a Frisbee a lot, but usually not well defined.
I've heard it argued that social security numbers when assigned, some people said "this is bad, the government can track people with them" and the counter argument was "no, this is just for social security payments, we're not going to use these for tracking individuals, but today, you can't have a conversation with the government without listing your social security number. Is that a true story? I have no idea, I only use it as an example.
There's generally speaking, 2 kinds of control, information and restriction. Information is simply "I know everything you're doing. I have recordings of all your phone calls, all your texts, all your medical records. I'm big brother and if you did it, I know about it."
Restriction (for lack of a better word) is more direct. "If you chop down that tree, shoot that animal, jump over this fence, walk onto that base, stay out past curfew or hack into that website, you will be arrested". Enforcement of laws that limit behaviour.
Climate change laws can take a few approaches. A tax on fossil fuels, a tax on incandescent lights, a tax on larger cars. Tax breaks for driving an electric car or installing solar panels. While it could be argued that any kind of tax is restrictive, it's not a very good argument. If that was the case, then larger government expenditures like military spending, and entitlements like Medicare, Medicaid & social security should be argued as government over-reaches. The people who say climate change is a government over-reach rarely extend it to taxation and government expenditures, so that part of the argument doesn't really fly. Taxation certainly can be restrictive. Over-taxation can certainly be a form of restrictive/controlling government, but if climate change works out to be a 1%-2% increase in taxes for an average person, that's pretty far from a compelling financial argument.
Laws that require carpooling might be seen as a nuisance, but again, that's hardly something the government does to "control" people, it can be done to reduce traffic congestion. A nuisance isn't necessarily a power over-reach. People accept the nuisance of greater airline security for example for increased peace of mind.
If the government was to track individual carbon output, which, there's zero plans to do, only corporate output, then what would that tell them? How much people drive? How hot they keep their homes? None of that information is particularly useful, as opposed to bridge tolls and EZ-Pass, which can tell governments a lot about when and where you are. Total carbon footprint in and of itself says very little. If they got super-anal, maybe they could see how many miles a person drives, but not where too. Again - that's not very useful information for spying on someone.
Any tax and any information gathered can be regarded as some degree of government power-grabbing, but ignoring the upside and just looking at what the government potentially has to gain by trying to tax and/or reduce carbon footprint, there's not enough information there. There's also the factor that the government has to direct resources and man-hours on this new task.
If the government tracks my internet surfing, and they do this to try to find Isis sympathizers, so they do it with everyone. If they record all my cell phone calls, again, trying to find terrorists or drug dealers by looking for key-words - that gives them a ton of information about me. If they know how much fuel I use - that doesn't tell them very much. If they forbid me from buying incandescent light-bulbs and I have to use those hideous florescent ones, that's annoying, but such actions to address an environmental threat aren't what I'd call a power-grab so much as a beneficial sacrifice (and last time I checked, I can still buy incandescent bulbs and if their cost goes up - I don't think a doubling of my light-bulb budget will kill my bottom line).
People are afraid of government over-reach, perhaps justifiably. But climate change and the proposals to address it, isn't a good example of that. That won't stop some people from making that point though. Fear, faux outrage and repetition often trump common sense.