Horse manure does, indeed, carry massive amounts of seed. That is, relatively fresh manure. The ideal way to use horse manure is to let it compost to nearly soil which will only work really well if it is mixed with straw or other bedding material. The first several years of my garden here, I had access to aged horse manure that had a good amount of fallen oak leaves in it - it was nearly soil and full of thousands earthworms who had been working very hard. However, it did not bring in the seeds that fresh would have because of the age. I will consider my garden blessed if I am ever lucky enough to have some like that again.
Steer/cow manure does not contain "sproutable" seeds in any great quantity because of the digestive system. What it may contain is hormones/additives not found in horse manure. I ordered it one year but didn't use much of it, it eventually completed composted so a part behind my main garden that should grow some fabulous corn if I ever plant there!
My preference is well-aged horse manure, but that is difficult to get unless you have access to mushroom compost which is the same thing.
The ideal combination would be to get horse manure, have an area where you can spread it with chickens to "work it" and remove the seeds. What you have left is a good mixture of horse and chicken manure with whatever dirt gets worked into it. The second year after the horse manure is dumped there, you would have the ideal fertilizer. But, and that's a big but, not many of us have the space to dedicate to processing it.
If you have close neighbors, chicken manure is out! I brought in a load of aged, foolishly thinking it would be okay. Fortunately, I had the foresight to have large planter tubs in the bed of the truck when it was loaded so we were able to move it with a minimum of "stink distress," but I had to cover it with heavy plastic weighted to the ground because of the smell. Even when we spread it on the garden the next spring and rototilled it in immediately, it stunk for several days. It was horrible. Fortunately, I have good neighbors who realized I probably hated it as much or more than they did. It was good for the garden, but I'll not do it again. As for chicken, what my own produce is all that will be in the garden in the future, and they mix it in themselves.
Just my observation and experience.
Glenna