My friend works with horses, I may be able to get some but then yes I’m not sure if I’ll be able to break it down... Is poultry much preferable? From what I read P seems to be higher (our P is pretty low).
As far as manure goes, you do want to be careful with the higher nutrient manures and when you apply them. Some actually are too high for direct application to a soil with plants and will burn the plants. This is because of high nitrogen. Poultry manure is pretty bad about this unless it is pelleted, which you might have some luck finding in stores.
I wouldn't try and apply a ton of manure in the first year to get your levels up fast. There's some risk of plant burning and you may over apply. Some crops also don't need a ton, leafy greens, etc. If you apply too much and then grow tomatoes, the plants will grow enormous because of excess nitrogen but produce little fruit.
If you have a fallow/not growing season (it looks like fall for you), apply the manure of any sort then, mix it into the soil, and the soil microbes will get to work breaking the manure down and storing it in stable forms in the soil. This will prevent burning. If you do the horse manure, you can apply a greater amount ahead of time and it will breakdown in the soil just fine. You may need to add some moisture depending on your climate.
One thing I did with a small garden a few years ago is I dug the area where I was going to grow potatoes a month ahead of planting and buried the horse manure under the ground by six inches under my potato planting trench (I was double digging). By the time the potatoes got big enough to reach down there, the manure had broken down very well and provided nutrition to the plants. I had lovely potatoes that year.
So overall with manure, apply and mix in ahead of time. Pig, and poultry manure tend to be "hot" in nutrients and need more time to stabilize before plants go in on it. Horse, dairy, cattle manures and pelleted poultry are less hot, need less time/no time before planting into them but provide less nutrients.