Animals Guide Transport (FS22)
Base game has animal transport trailers for horses with two horses on each trailer, then basically small and large trailers for cows, sheep and pigs with lower and higher amount of animals transported. Larger trailer transports 12 cows, 36 pigs and 38 sheeps. I have to assume this is one type of animal at the time. There are no chickens mentioned and chickens cannot be transported.
Animal transfer from one enclosure to another. You can edit placeables.xml file at husbandryAnimals clusters property has your animal xml lines, just simply in-game buy a new animal enclosure, rename it so you know which one it is, save game, exit, edit placeables.xml and move wanted animals from old husbandryAnimals clusters to the new one. This is not cheating because there is no proper way to transfer animals from one enclosure to another, yes you can use semi-truck pulled wilson silverstar animal transport trailer, but if you have hundreds of animals not to mention thousands and this keeps repeating every few months... yeah that semi-truck hauling is not really an option. You could also sell specific set of animals and then buy them right back, this of course costs money and its kind of weird way, I mean they are not the same animals in that sense anymore if you sell 100 cows and then buy back 100 cows right away.
Animal transport wilson silverstar is working nicely though, just drive the trailer over the animal paw icon which brings up the R option to bring up animal dialog. For example in sheep barns you back up the trailer to this icon, strangely enough even with chickens this icon came up while silver star was above it even though you cannot transport chickens (trailer does not support the animal type). Once silverstar dialog is up, you have list of animals on the right side, these are not sorted in any way, so if you want to find lets say the youngest animals, you just have to browse through all of them. Once you found the animal(s) you want to transfer, click select button (RETURN) and number of animals dialog gets highlighted, if you want to move all the animals its easy to just click minus key "-" once and the highest number of the animals is selected, then just press SPACE to "move to trailer". Once you're done, animal 3D models appear in the trailer, nice. Now just move over to the other barn / building or animal dealer selling point and activate animal paw dialog to complete the transfer or sell. Animal transport trailer is actually pretty straight forward way to transport animals between barns and animal dealer, however there is the limitation of really big cattle operations, you don't want to haul 12 cattle / cows at the time if you have thousand head herd.
Animal transport wilson silverstar or silverSATAN... another time I distributed my 270/270 big pig barn into another barn, wanted to divide it by two at least, well after TWO loads of 36 pigs each using that awful conzole GUI to operate the transfer... I'd just about had it, it is just so painful game-play to transfer those animals using wilson silverstar even though it is realistic vehicle and all, you just do not want to do that many times in your farming simulator life time, its too cumbersome and painful. I much rather do the savegame and edit placeables.xml dance than this silverstar GUI crap 
There is a mod out there like "animal cane" or something, which is a very small hand held cane you can pickup and carry around, this is actually a vehicle where you can transfer animals just like in wilson silverstar. Sounds excellent, right? WRONG -Arnold Schwarzenegger voice. It sounds great on paper but this mod doesn't work in practice, when you are carrying the cane it will drop to the ground constantly and very often it disappears under ground, now you have to reset it back to the vehicle shop and as we all know, the contents of tanks, trailers, hoppers etc is emptied out during reset, so your animals go "poof" into the oblivion. A real shame because the "animal cane" is a brilliant mod for handling hundreds of animal transfers, just too bad it doesn't work, its giants engine physics for ya