Weeds is a matter of interpretaion. In my area , hay is coastal bermuda grass. Any place i add horse manure, i get bermuda grass. Not a good thing cause its hard to get rid of. Where i placed a hay bale for the cows last winter is now a 6ft circle of bermuda. Its a pasture grass , a lawn grass, and a weed in a garden or orchard.
Im not concerned with any manures that come from grass eaters. I apply it fresh or rotted.
Im not concerned about medicines, but many are. I have nothing to back up my lack of concern.
Since it has to be transported, leave it in a pile for a month and turn it if you have the means. The heat should resolve most of your concerns.
A local company used to sell
compost made from the local 4h shows. I was happy with the results