There is a big difference between manure from ruminants (e.g. cows) and non-ruminants (e.g. horses, chickens, etc).
Non-ruminant herbivores produce poo which is relatively bulky and contains a lot of undigested plant material. This material is degraded rather quickly by bacteria, but until that happens the manure is traditionally described as "hot", and indeed if it is stored in bulk it can become physically very hot because of the biological processes going on in it. In the 19th century horse manure was the standard way to grow tropical plants in "hot-beds" or "hot-houses" in temperate climates - just plant them into neat horse-manure that would easily heat up to 50 degrees C or more.
Using it in that state is not a good idea for root veg, because it may cause cosmetic surface damage to the roots. Also it is releasing a big rush of easily absorbed nutrients which can cause distorted growth (e.g. forked roots), or induce the plant to flower (bolt), set seed, and die while there is a lot of food available for its seeds to germinate, instead of slowly storing up food reserves in its roots which is what you want it to do.
Manure from ruminants has already been "reprocessed" several times before it leaves the animal, and is therefore less bulky, often has a high water content until it has dried, and has a lower nutrient value - but it is still useful as a soil conditioner.
Aside from any issues with pathogens, you can use cow manure for root veg pretty much "straight from the cow," but horse manure needs to be stored (which is effectively the same as composting it) until the bacteria have finished doing their thing with it, and it has (literally) cooled down. Most of the pathogens will have been killed by the heat.
Using "chicken feed" as manure seems a rather strange idea - unless you are letting some chickens process it first, of course!