Glad to hear it's going well. I've dealt with the odd feral/rescue baby in my time and am quite old-fashioned, I don't do 'training' as such until they're at least 3/4, can't be doing with tickling them with carrier bags on sticks and the like, they tend to come good in time just mainly being left alone, you don't need to over handle them just because they've missed a little early education. So long as crucially they are having regular pleasurable/non threatening (mainly food related!) associations with people and are kept with friendly, well handled other horses you really don't need to do that much more - his natural unclipped coat should do the job of a rug until such time as he's actually working so I wouldn't worry about that - do you need to move him around much between fields/yard etc or can he settle in one place (the latter much better if you can manage it). Does he lead OK if following other horses or is that a bit hazardous ATM?
Some of the feral/anxious ones I've dealt with come around to humans being actually quite nice and unscary quite quickly and if left largely to their own devices as above will be quickly approaching you looking for food and fuss and you can build up to handling their head, ears, feet etc gradually from there, others take much much longer and prefer to remain at arms length - it's all personality types and what their past experience has been (benign neglect vs actively being frightened/abused) but either is OK, if he's only a weanling you've got years before it becomes a necessity to do much with him.
So I'd drop any anxiety about training for now, just treat him like one of the herd, if the others come in it will be good for him to be stabled occasionally next to a quiet friend and with grub so he can see that nothing terrible happens, if you need to catch/move around the others then leaving a leather foal-slip/field safe type collar on him so you can grab hold if needed is probably sensible, otherwise just plenty of grazing and play is all he really needs for 2-3 years yet.
If you do urgently need to do anything with him, farrier/vets etc (although like a PP said baby hooves are quite soft and if he walks on hard ground reasonably often you may get away with not needing too much intervention) then there are fantastic sedatives available these days which are very safe (standing sedation so they don't get completely knocked out/go down is best). Some vets seem more reluctant to use it but I'd much rather do that personally with a very nervous animal than rush them into more handling that they are comfortable with, horses can very much go over the top into panic/flight mode and then that can undo all your good work getting them calm and trusting. Whereas if he's high as a kite/sleepy 
your professional can come in safely and quickly to do what they need without anyone being hurt or traumatized....