He's lovely! Fellow small hairy cob owner/lover here! So the feather does take some maintenance to keep looking nice esp in winter, feather mites can be a problem to watch out for especially if they've been a bit unloved or living in a big herd where they can spread, mine were rescue cases and both had had them badly, very itchy and uncomfortable for them. Like with nits or any other parasites the best tactic is prevention, so to vigilant and catch any infestation early, wash with medicated shampoo if you do spot any bugs - if that doesn't do the trick there is a Fipronil spray that's for fleas in dogs/cats really but that works on mites too, or last resort the vet can give a course of injections that kill them off. But hopefully your boy will never get them!
In summer you may have problems with flies/sweet itch causing him to rub at his tail/mane, I don't think there's any particular reason why cobs would get this more than any other type although anecdotally I do think they seem more prone - perhaps it's just more noticeable when you see the unsightly rubbed patches in that lovely thick hair! A good fly rug and hood, and oodles of fly spray are a good investment if he is bothered.
The other end of the spectrum is winter care, I'm in constant quest of good dry grazing because the mud is such a pain in feather-y hairy legs, mud fever can be an issue - contrary to popular wisdom this is actually a mild skin infection caused by the bacteria in mud rather than a reaction to the mud itself, opinion seems divided on whether feathery legs gives them a degree of protection or makes it worse because the mud sticks to the feathers and therefore is kept closer to the skin - either way I like to try and keep their legs as clean and dry as I can manage and be super vigilant about plastering any small nicks, cuts or grazes on the legs in anti-bac and sudocream as this is where the infection will get in. Pig oil is popular too on the idea that the mud will slide off easier but can't say it's ever really worked for me on our heavy clay but it does also help prevent matting as well...
Grooming wise I do tidy up my girl's whiskers/beard and legs very gingerly with scissors (well one of them, the other is retired now so is allowed to be fully au naturel and never let me very near her with pointy objects anyway!). For showing at local level he can do coloured pony classes, riding club horse/pony, family pony and all the 'fun' classes like best mane and tail (he's probably a shoe-in!), pony the judge would most like to take home. I wouldn't worry about cob classes, it's not so much that gypsy/vanner/traditional cobs 'can't' enter those classes but show cobs are a different type entirely really, they're usually fully clipped out, hogged and trimmed and also are bigger than your boy. If you wanted to get more serious about showing CHAPs would be the way to go or some larger shows do have classes specifically for traditional cobs also...