You don't need a meteor to lower temperatures
I want to introduce you to the year 1816. Also known as the year without a summer. In short, there was a volcanic eruption which expelled a lot of sulfite dioxide particles in the atmosphere. These particles reflected part of the light that came to Earth, thus cooling areas underneath. Areas that covered large parts of the northern hemisphere.
However, that's not good
The "without a summer" part of the name is not at all coincidental. And it's putting the effects mildly. It doesn't just mean that you skipped going to the beach this year. Effects included:
- snow in the month of July
- frost and low temperatures led to a lot of crop failures
- people lost a lot of money, especially those who were doing agriculture but sectors suffered as well
- people starved to death because of the weak or non-existent harvest
- other people froze to death because they weren't prepared to warm their homes in the summer
Another name for 1816 is "eighteen hundred and froze to death". That better helps convey just how bad "no summer" can be.
Undirected changes are not good
The global average temperatures in 1816 fell by only something in the region of 0.5° C (0.9° F). It's a relatively minor change when you look at the numbers, yet the effects were catastrophic. That was not directed in any way.
A meteor hitting Earth to try and plunge the global temperatures down would lead to an even bigger catastrophe. It would have even less of a direction in terms of effects. In addition to the temperature change, you'd have the impact to deal with which can wreak all sorts of havoc. It depends on what the meteor is, how big it is, where it falls, etc. All things you can hardly account for. I doubt you can even account for what temperature shift you'd get from it.
All in all, if we can't even manage when only the temperature changed alone, I don't see how dropping a big rock from the sky and hoping for the best would work out.
But maybe you can direct the change
Thanks to 1816 and science, we now know a lot more about what particles can do in the atmosphere. If you have some way of introducing more sulfite dioxide particles at a very tightly controlled rate, you can cool the planet. If you can somehow get rid of them, you can warm it back up. So, you might be able to beat greenhouse gases by bypassing the problem entirely. In effect, you will have a "thermostat" for the entire planet and even though greenhouse gasses retain heat, you can set the "thermostat" slightly lower to compensate for that. And then turn it back up before it starts snowing in July.
That is likely to be a huge effort. I don't even know if we have an idea what technology is needed to achieve that. Moreover, it doesn't really solve the core issue - that would still be there. However, a civilisation advanced enough to be able to direct a meteor down to their own planet, and crazy enough to actually do it, could probably go with a "global thermostat" instead. It's still better than their other plan.