All the usual stuff, leading, tying up, bathing, clipping, spook proofing - my barn looks like a fairground sometimes with bunting hung about the place, flags flying in the paddocks, people walking about with umbrellas, riding bicycles around, quads, tractors etc, etc.
Obviously rugs, rollers, bandages, mine are saddled, bridled and walking in hand tacked up by 18 months. Loading is very important for a youngster to learn, as is learning patience eg, when tied he stays tied for as long as I want, if I am leading on the road etc and I stop to talk then I expect a horse to stand beside me and to switch off. Not eat, not fidget, not move - just stand, preferably ground tied.
Get them used to walking over obstacles, my babies are used to poles/cavaletti in their gateways from birth. Teaching a youngster to look after his own feet is important too, make them walk over logs, raised poles, under low branches, through narrow gates, up and down banks, over ditches, through puddles and streams.
Whatever you expect of a trained horse can be started with a baby, in hand, just for a few minutes at a time, daily or three or four times a week, you take nothing away from his being a foal, he has another 23 1/2 hours in the day to be that.
I am horribly hot on manners, I expect feet to be lifted when I ask, a horse to go backwards, sideways, step up etc and it doesn't sound much but one of the best things you can train a horse to do, after tying is to lower his head on command.
Oh, and if you can, find some cows, pigs, donkeys, llamas etc and deal with that at a young age too.
Ditto Enfys - by the time I sat on my pony the first time, he'd already done everything on the ground that I'll ever want him to do under saddle. And it's working - I rode him last night for about the 10th time (5th time without a ground person) and he was going forwards off the lightest brush with my leg, stopping off a thought, did a lovely turn on the forehand and a passable attempt at turn on the haunches. He's hacking out alone and in company and there isn't much that phases him
Horse agility is a great way of bombproofing a baby in a safe environment, but nothing beats long walks together in the countryside (in hand) to build a bond, develop braveness and teach the horse about the world he'll be hacking out in later in life.
I love training babies - it's so rewarding to go from spooky little foals to sensible riding ponies: