[RPG] Are there specific skills required to tame mounts

I agree with Hey I Can Chan, this really depends on the campaign - and on the specific city in question. That's something you should ask your DM.

Note however that on the Pathfinder SRD entry for undead, the list of "Five Things Almost Everyone Knows About Undead" contains the following:

The following are a few facts that are considered common knowledge among civilized peoples.
[...]
3. Undead are invariably evil, as are the means to create such beings.

This list represents the beliefs of most "civilized peoples" - not necessarily the truth or the beliefs everyone, but it does set the default on "yes, it is evil to ride an undead mount" - if that holds for your game may of course vary.

Also, note that skeletons, zombies and many "mount-suitable undead" are always evil aligned - so your mount will always register as evil if anybody uses detect evil or something similar on it (and with a moderate aura if it has more than 2HD)...

As far as I can tell, rules are scarce on this subject. All we have is:

PHB, Chapter 5, page 144: (on wearing armor, in general)

Armor Proficiency. Anyone can put on a suit of armor or strap a shield to an arm. Only those proficient in the armor’s use know how to wear it effectively, however. Your class gives you proficiency with certain types of armor. If you wear armor that you lack proficiency with, you have disadvantage on any ability check, saving throw, or attack roll that involves Strength or Dexterity, and you can’t cast spells.

Summed up: Anyone wearing armor must be proficient, or face the consequences.

PHB, Chapter 5, page 155: (on barding as equipment, price)

Barding. Barding is armor designed to protect an animal’s head, neck, chest, and body. Any type of armor shown on the Armor table in this chapter can be purchased as barding. The cost is four times the equivalent armor made for humanoids, and it weighs twice as much.

Summed up: You can put armor on an animal, and it's price is four times that of normal armor.

PHB, Appendix D, page 310: (variant rule on warhorse specifically)

Variant: Warhorse Armor An armored warhorse has an Armor Class based on the type of barding worn (see chapter 5 for more information on barding). Its Armor Class includes the horse’s Dexterity modifier, where applicable.

Summed up: A warhorse can wear armor. Warhorse, as opposed to Riding horse. Since this is a variant rule, it implies that without the variant rule in effect, all animals (not only warhorses - and war-dogs, war-elephants etc too, I presume) can wear barding.

But do they require proficiency? As per the general rule on armor proficiency quoted at the top; yes. How would an animal go about acquiring such a proficiency? We're not told. Also, we're not told what the difference is between a riding horse and a warhorse, and if/how the first can become the latter.

However, when the RAW is lacking, we just keep rolling. The spirit of the game has always been "make it up as you go". So here is what I would suggest: A non-war-trained mount is not proficient with armor. A war-trained mount is. I believe this is relatively consistent with the rules above.

Also, we need to come up some rules for training a war-animal. Say a month or two of rigorous training in the hands of a skilled person?

Yeah, and just so I've mentioned it: A lawyer might argue that barding and armor are two different things. I'd argue that it's the same thing with different names, depending on the wearer.