I choose winter due to our climate and humidity in Florida...it's easier to put up a heat lamp if it's really cold and they choose to Lay by it, than see the goats (and us) deal with the heat and humidity during kidding...
People tend to forget that we all don't live in the same climates or have a abundance of pasture to rotate our animals in....some of us are truly back yard herd people and have to adjust things to suit our climate and management needs...not always "by the book" but it works
You didn't mention kindling, but I'm sure you mean rabbits too? I didn't complete your survey either. Just getting started with the rabbits, but intend for it to be pretty much year round, except last of July, first of August due to heat.
Chickens? No roosters here. I'll stick with getting day olds. Let someone else bother with incubation and broody hens. Day olds are just so inexpensive AND reliable. No waiting, hoping, candling, and ending up with all cockerals. And if one ends up a cockeral anyway, I get to bi!@# to the farmstore/breeder. Ditto with the ducks. Besides, Runner Ducks seldom go broody anyway.
Goats are coming in the spring. Wethers or nannies. I've seen the worry/aggravation folks go through at kidding here on BYH. NO THANK YOU! Just eat the brush, and then I eat you. Next year somebody will have replacements.
So. Piedmont area of SC. Mild climate. Extremes? Mid 20s Jan & Feb, lower 90s July & August. Pretty nice if I WANTED to breed....just not worth the pain, worry, and aggravation to me.
As a former boss told me when I tried to explain things. "I don't want to hear about the labor pains. I just want to kiss the baby".
Spring, summer and fall is what we do with our goats because we need milk year round. We usually plan for a bunch in fall so we can go strong though the winter. Not fond of dealing with kids in the winter as it can get pretty cold here.
The sheep only lamb in the spring.
I lamb and hatch in the spring and am playing with the idea of an Oct. lambing session as well, at least for some of the sheep but not all. April and Oct. are high forage months, with the most lush graze and no flies or excess heat, but no cold weather. A little rainy at times but on clean grass it's not an issue.
Hatch only in the spring, as fall hatching leads to young chicks out on the land around the time the migratory hawks are coming through...hungry and looking for food about the size of a 2-3 mo. old chick. Most losses I've ever experienced in 44 yrs of chickens was done all one fall after a fall hatching. Never again. Hatching in the spring, when all other young are plentiful on the land and the crows are protecting their own young insures no losses to aerial preds.