This is a question I've been wondering about for a while. If I wanted to give my characters the best possible chance of surviving my story's Armageddon, what time of year should I schedule it for?

Let's keep the scenario as general as possible for maximum usefulness to people who aren't me, while still laying down some ground rules. Let's assume some sort of global EMP attack / solar flare that destroys the entire world's electronic infrastructure. No radiation, no explosions, no immediate deaths. But everyone's left without electricity, running water, sewage, and every other part of the vast network of societal services we perpetually take for granted that keep us from having to fight every day for the right to breathe. What's left of the government is rapidly breaking down, the stores aren't restocking, and people have to secure access to food, water and medicine, acquire the means to defend themselves from others, etc.

Let's further narrow it down to focus on the USA, since I know that the seasons are wildly different depending on where in the world you are, and lots of other factors could be in play to make the answer a great big "it depends".

What time of year should I have this event take place in to make sure that the greatest number of people has the greatest chance of living to see next year?

Mid Spring

Around late April the last freezes will have passed through the U.S.. It will be possible to remain outdoors with little protection for seven months from this time.

Farmers will have already prepared their fields (which would have required the heavy equipment) and planted the first crops of the year. Setting up manual irrigation will not be an unbearable challenge. Soy is ready for harvest in a month. There will be time for multiple plantings and harvestings of this staple calorie crop in rural areas, and also plenty of time for urban areas to establish farming in any areas suited for it.

There will be plenty of time to build new things. Most sewage systems are based on gravity allowing everything to flow down hill. With a little work, people may be able to get sewage and water working in places where there is easy access to springs, rivers, or mountain runoff.

There's also plenty of time to prepare for a winter without heating. Time to chop wood, knit blankets, buy extra clothes, can food, make candles for the long periods of darkness.

Christmas (seriously)

If we narrow it down to North America in particular, there are several advantages to this being your chosen date.

1) Family

Christmas is often seen as a time of family, so small family gatherings are happening all over. This is actually a good thing, because less people are going to be out trying to find loved ones, and those you care about are already grouped together in a small 'clan' that is determined to look after each other.

2) Food

These aforementioned families have already stocked up for the Christmas period and therefore have an advantage in terms of managing food supplies going forward in the initial chaos while they work out what to do next to sustain themselves.

3) Cold

Sure, not nice to be out in, but if the power goes out, all that aforementioned food hoarded by the aforementioned families will go off at a slower rate. Still not good if you're in (say) California, but in Illinois or New York, you could almost freeze your food by leaving it outside.

4) Traffic

Because the families are already together, there's little need to travel meaning that the roads are freer for the emergency services, assuming of course they can get their cars and trucks working. That means that as issues arise, the emergency teams can respond more rapidly than they could if everyone was trying to get to family or just plain get out of dodge in a disorderly fashion.

The Caveats

This is still a catastrophic scenario by most standards. Large population centres (cities) consume a lot of food, and produce almost none. Many of the people in these population centres start dying after a few days no matter what you do and civil disturbance will be on an exponential curve when the food starts running out. Add to that the fact that the cold is a two edged sword insofar as our warm-blooded metabolisms mean that we need to eat more during the cold than otherwise, so that food that lasts longer before spoiling gets eaten faster to avoid starvation.

Also, EMPs and other technology neutralising phenomena will make it much harder to coordinate responses and the like, and most of the people who survive from the cities will do so by walking out of them immediately. Some of those families (for the reasons mentioned above) will be less likely to do that at Christmas.

The real winners out of a doomsday scenario at Christmas in North America are going to be the small communities across the food belt of the USA, where they have family around them, a supply of food and the capacity to grow more as they go, not to mention having herds of cows and sheep to survive off while crops regrow.

September

Summer is a busy time when people are unsettled and often off traveling. Kids may be separated from their parents. A lot of people move in the summer. But once school starts, people are pretty settled in for the year. Even people who aren't in school or parents of children in school (or working in schools) tend to move with that schedule.

In cold weather areas, crops are mostly in by September. In warmer parts of the US, a lot of crops ripen year-round or specifically in the fall months, but food and survival temps aren't as critical in winter.

Because of "back to school" and the end of the travel season, stores are well stocked with goods of all kinds.

Summer heat is more or less over (sometimes you get a last hurrah) so super quick food spoilage, issues with sewage, trash, and corpses (the event may not have caused deaths but people die anyway), and the death of fragile people from not having air conditioning are not strong concerns.

It may be cold at night, depending on the location, but it's a few months before the worst of winter and accumulation of snow. This gives people some time to prepare. September is a great time to can food (and there should be enough fuel left to do it) and semi-perishable foods can survive outdoors, at least overnight. It's a good time to cut wood and prep fireplaces (for those lucky enough to have them) for use. Some may be able to buy wood stoves (there are some designed to use existing chimneys) which are far more efficient than fireplaces and allow cooking too. Some families will move in with each other to conserve fuel and other resources.

For local communities that choose to work together under effective leadership, everyone should survive the winter (aside from some with severe medical conditions). If people don't panic and if government stays intact, a lot of places will be able to function.

Small rural towns are the best bet as they're likely to have horses or oxen available, may grow their own food already, have wood for heat, and don't have too many people to fight over resources like generators and fuel for cars and trucks and tractors.

Cities will be in trouble because most food must be trucked in and cities have more complex infrastructure. And potable water...big problem. Their survival will depend on a lot of things but having the event occur at the very end of summer is their best chance.