Raised bed soil is a lot like normal soil, but it is more rewarding if you treat it well. Adding any kind of compost is important!
Any advice from people with experience getting raw manure from neighbors would be better than my opinions. But here they are anyway.
I might have preferred to compost the manure first, but I think many people will tell you that's not necessary. Just don't add more than 2-3 inches per season, as a guess. What do other people think? How much would be too much, if you till the manure in 12 inches or so?
Maybe 2-3 inches tilled under in the spring, and another 2-3 inches in the fall?
Maybe top-dress with 1 inch of aged manure in-between?
Or set some raw manure aside to compost for fall and next year. It will go even farther if you add paper or sawdust or leaves or grass clippings. Then just lay the compost on top of your raised beds and let worms come up to eat it and drag it underground. Like a dissolving mulch.
Many people will say you don't need to till once the soil is highly organic. I've never gotten that far! I have to fork or spade my clay every year or so to break it back up.
I've been told by many people that we should worry about whether the horses ate hay or straw drenched with lots of persistent herbicides, and to worry about whether or not the manure had lots of weed seeds.
I've never had the opportunity to get my hands on manure without paying over a dollar per bag, I would grab that manure and it would be in my compost heap so fast the horses wouldn't have time to get out of my way.
I think the value of testing is to tell you how much lime you need, to adjust pH. And maybe to tell you that you ALREADY have enough N, P or K, so stop trying to reach a toxic level.
