There are a few forks.
In the short term, some humans may adopt a sea-based hunter-gatherer survival strategy. Existing expertise with fishing is key here. The oceans have a lot of thermal mass, so they will take a longer time to freeze over.
Another short term strategy involves greenhouses and copious use of energy. Geothermal power will function (until things break down), and nuclear power with its insane energy density could hold up pieces of civilization. The hard part is maintaining the supply chains to keep everything working under catastrophy and chaos.
As time progresses, things get worse. A winter is different than an ice age. In a winter, the snow melts eventually. You can just push the snow aside, or gather it in an out of the way place, and wait.
In an ice age, there isn't enough space to push the snow aside. It continues to build up. Glanciers form, and the ice becomes geological. The ground, which contains minerals and organics, becomes buried and out of reach to surface organisms. Deposited organics gets buried under yet another and another layer of snow and ice, and becomes lost to the surface biosphere until melting occurs.
Even a sea-faring people need new materials, and even northern hunter-gatherers live on the land and get resources from it. So the sea-faring hunter-gatherers will be frozen out by the glaciers.
The nuclear and geothermal bases can continue a war of melting. If a good chunk of a continent can be covered in such nuclear/geological powered colonies the glaciers could be held back. But as ice flows towards gaps, you basically need to melt an entire continents worth of precipitation.
Total world rainfall is 5E14 tonnes. Melting water is about 300J/g. So to melt the world precipitation requires 5E15 watts of power. This is a K type 0.9 civilization, beyond our current budget. And way larger than what can be produced by geothermal (5E13) even theoretically.
The thing that can save us is that precipitation has to come from somewhere, which requires sublimation or evaporation. As the world freezes over, less and less water vapor will escape into the air. Clouds will die out. Solar power will become more practical.
The source of the ice age now matters. With clouds discounted, the sun's radiation will beam down on the Earth. The white earth will reflect more light, and together with if the sun's output is reduced it could explain a continued ice age.
Use of solar power at this point could help with pushing back the glaciers. But turning solar power into electricity, then melting ice, is less efficient than just heating up the ice directly. Put coal dust on the glancier tops and let the sun heat them up.
In the long term, things get worse. The oceans surface can freeze up, followed by deeper portions. Vents at the bottom of the sea remain melted, with liquid water volcanoes sometimes reaching the surface. All other life is gone (except possibly human nuclear/geothermal bases). Some think this may have happened in the past. The natural way to get out of it is to wait for vocanoes to emit large amounts of greenhouse gases, like CO2. With everything covered in snow and ice, weathering (which naturally removes CO2) and plants (rare, which consume it from the air) are missing. So the CO2 levels in the atmosphere build up to seriously large levels and the greenhouse effect kicks in. Things warm up, glaciers melt, albedo of of the Earth drops, things warm up more. If albedo drop outpaces weathering+live, the world continues to warm up. Eventually weathering+life+radiation start slowing greenhouse faster than albedo increases help it, and the world stabalizes with a melted ocean.
So a long-term defence would consist of finding artificial greenhouse gasses and terraforming Earth.
In the epoch term, whatever led to the cooling of the Earth may not be satisfied by simply painting it black. If the sun is dropping to 50% of its current brightness somehow, no amount of coal dust or greenhouse gases will prevent an iceball Earth.
Humanity would have to climb up to a K1+ civlization and stop being planet bound to survive, all while trying to live through a catastrophe. Desperate measures and technological revolutions would be required. Human extinction is by far the most likely result.
In the short term, non-industrial civilization could survive, but in the medium to long term only an massive industralized response to this crisis could surive. Things would be very precarious as a breakdown in any supply chain could wipe out all of humanity, and supply chains would be extremely hard to maintain over the frozen Earth.
It would take civilization-scale effort to rescue the human race from a rapid, total and unending ice age. The odds are we wouldn't survive, and at the least the vast vast majority of humanity would die. If we did survive, the civilization that emerged would be as different from today as modern industrial civilization is from ancient Egypt.