Horses are separately counted and limit the availability of mounted troops, but in practice there are usually way more horses than you could ever want.
Generally, T5 and/or Level 20 and above are considered veteran, but this is only a rule of thumb and the current troop trees contravene this frequently. There are 3 kinds of recruits: peasant, veteran and mercenary. Villages are much less important as recruitment centers than in vanilla. The types of troops available from villages is influenced directly by the kingdom slavery policy. Units come in tiers, from 1 to 9 (though generally T3-T4 is the lowest kind of battle-worthy troop type you will see). In v0.26, troops are recruited directly from towns and castles, and to a much lesser extent from villages. This is based upon my own gameplay experience and information gathering. I've decided to just put this information here in case anyone needs or wants it.