Well I actually disagree with some points about how much you could be doing right now, that will pay off big time in 3 years or so.. I don;t agree with overloading their young minds with too much information etc. and would never actually 'start' anything much before its 3rd birthday ...BUT..I really dont see short and gentle ambling for moderate distances as doing too much at all with a foal. After all if you are already taking the mare and foal to shows etc, you very soon ensure it will lead nicely and sensibly, so what is the difference here - if you are walking them out on the showground with their dam..or a couple of months further down the line, when it has been weaned, out and about around the immediate vicinity of where you keep the foal - obviously not dragging it along the road next to jugganauts etc.
Back in the day when I had youngsters around, after initial handling when they are weaned and getting them very used to walking nicely in a head collar around the yard - I would very often walk foals of this age up the bridleway from their field and just allowed them to stand and graze at the side of the hedgerow whilst traffic buzzed past , very often myself or another family member would ride a trusty old timer up alongside them for reassurance to start with.- total distance probably about 500 metres or so there and another 500 metres back......usually then just faff about brushing them before going back in their field. Huge help when later down the line you start taking them off the property and out into the big wide world IMO.
But as always we all differ hugely in what we would and wouldn't do, so long as nothing is harming the horse or foal in this instance, then I would do as I have outlined above.