With an abundance of sustainable and reliable energy, survivability of an event such as a volcanic winter would be drastically increased. Energy is the only limiting factor in producing a 100% self-sufficient and self-contained living environment, not only in space, but on earth as well. Energy availability would be instrumental in facing such a disaster, and with adequate preparation we could manage quite comfortably.
However, if the green dream of a world powered exclusively by renewables were realized, humanity would have no hope whatsoever. The lights would go out indefinitely, and any sort of civilization would promptly collapse, with only a handful surviving in miserable conditions. Renewables are not reliable, and are incapable of sustaining civilization through such a crisis.
While efficiency is a laudable goal (to which most engineers already aspire), eking by with extreme conservation is highly anti-productive, and exacerbates environmental and societal problems. Energy is not a disease to be eradicated, but a resource essential for enabling greater levels of recycling and reuse, and ultimately a sustainable high quality of life with minimal environmental footprint. With prosperity, population also tends to level off, solving that problem as well.
Energy is only a problem when it is derived in an environmentally destructive manner, as with mining and extraction of fossil resources, or the vast and inefficient collection, storage, and distribution infrastructure for wind and solar. These sources also require extensive mining for the raw materials comprising the infrastructure, and the fuels required for transportation in both cases.
Owing to a far superior energy density, nuclear energy necessitates very little mining and supporting infrastructure. Molten salt reactors like LFTR use nuclear fuel roughly 200 times more efficiently than todays LWRs, and with passive safety and no need for water cooling, they can be sited virtually anywhere. For perspective, a 1GWe LFTR plant would be roughly the size of a Walmart. Incidentally, there are upward of 10,000 Walmarts, which would accommodate 10TW of LFTR power production--enough to provide for 10 billion people at US per capita power consumption.
Each year, a 1GWe reactor would only consume about a ton of thorium, and produce about a ton of fission products. All of the fuel required to power the world for a year could be mined at a site not much larger than a Walmart itself. However, it could instead be recovered from the tailings of rare earth or other mining already in progress. (For reference, a metric ton of thorium fits in a sphere 55cm (or 1.8ft) in diameter.) A plant could easily have decades worth of thorium on hand.
Of course, the picture wouldn't be complete without considering the waste. A single GWe of generating capacity is enough to power a sizable city, producing 1t (metric ton) of fission products per year. One might worry that these are going to accumulate and produce an intractable problem, but in reality the radioactivity is constantly disappearing, and will reach a steady state when the creation balances the decay. As 83% of the fission products of a LFTR are stable after a decade, and the rest no more radioactive than ore in 300 years, the sum total of waste produced for one GWe of power, will gradually build up to, yet never exceed 59t after 300 years. This is a trivial amount, which is still overstated as many of the fission products have uses. (radioisotope thermal generators, sources for medicine or food irradiation, etc.) Even if politics prevents doing something useful with it, it could still be safely stored in a small room on site.