Hi!
It is great that you are trying to think this through but unfortunately while your idea looks very tempting at first glance, there are lots of very basic and very practical considerations that unfortunately speak against it. As always, the devil is very much in the detail.
I know of only one outdoors free-roaming set-up in Germany that is outstanding; even that has access to a large indoors room for the winter, weather extremes and for caring for the ill and frail. It is fully enclosed with aerial protection and takes a whole team of dedicated volunteers to keep it going even though it is a private place and neither a breeder nor a rescue. The recent record summers and massive droughts have been a huge challenge, which is only going to get worse; especially when there is a sudden jump in extreme temperatures like the one in Canada. Germany has already had 35 C in June this year...
Faszination Meerschweinchen
My biggest consideration would be that guinea pigs are not hardy and that they are definitely not heat-proof. They are also very vulnerable to anti-social activities outside of school hours. We hear pretty regularly of attacks, break-ins, hutch theft (with the guinea pigs still inside) or even arson on hutches and guinea sheds. School property makes that even more likely and inviting. Human predation is an issue that needs to be taken very seriously.
You will also require aerial protection; they are no safe to live in a run open to the air. Rats will kill guinea pigs if they can get at them - an open hutch or run is a clear invitation to do their worst. Keep in mind that they can get through very small cracks. We are contacted with distressing regularity by owners of outdoors piggies who have found theirs dead in the morning and evening, for no apparent reason but likely from a sudden bad fright due to a predator trying to get into the hutch. We have also seen videos of foxes getting over those kind of fences you have.
Guinea pigs are a species that has evolved living in thick undergrowth that is well insulated against the extremes of weather; they don't have the most efficient way of regulating their body temperature and react quickly to larger swings, whether that is seasonal or just larger day/night jumps.
They are crepuscular as a species; i.e. they are most active at dawn and dusk (when temperatures are at their most moderate) but spend the middle of the day and the nights mostly resting/sleeping and digesting with the occasional quiet browse - that means that school hours will coincide with their day resting period. They also move from their denning area to their feeding grounds in larger herds along paths in the undergrowth and instinctively avoid wide open spaces because they are very vulnerable to predation from aerial or larger predators there.
Guinea Pig Facts - An Overview
Then there is the issue of climate change - is it really appropriate to keep a species that struggles with the extremes of weather outside in an increasingly volatile and unpredictable climate? Guinea pigs are neither hardy, don't deal well with too much damp weather, storms, fireworks and definitely don't cope well at all with the heatwaves and heat spikes we have seen in recent summers when we have been inundated with distraught owners and people with piggies with heat stroke or life-threatening heat exhaustion wondering why their piggies were lethargic and not eating. Cavies need protection in much lower temperatures than you would expect. The traditional moderate UK summer was fine for piggies to live outdoors. The new world sadly isn't.
In the age of massive and very rapid climate change, outdoors piggies are extremely vulnerable to the extremes of the weather.
Hot Weather Management, Heat Strokes and Fly Strike
Cold Weather Care For Guinea Pigs
Unlike the wide-spread held opinion, guinea pigs are neither easy nor cheap pets. They produce A LOT of poos in both runs through the gut they need to fully break down and digest the tough and nutritious hay/grass fibre that is the mainstay of their diet; good quality hay is not quite cheap - especially not at the amounts they go through.
They will need keeping a daily eye on them and a weekly weigh-in and health check as they can gown downhill very quickly, round the clock syringe feeding support when very ill and their vet treatment can quickly run into the hundreds of pounds once you are looking more complex medical treatment (especially longer term twice daily medication) or a life-saving operation. Do you have that kind of dedicated time and the budget to cover these welfare needs? The biggest life-time budget in any pet's life is vet care. There are no cheap pets. If you want to provide an example of animal welfare, then you will have to address all five animal freedoms.
Piggy trios are the most difficult constellation to get right. So that is unfortunately another spoke in your wheel; especially as no good standard rescue will rehome already stably bonded piggies into a school setting.
Boars, sows or mixed pairs; babies or adults?
Rescues, Shops, Breeders or Online? - What to consider when getting guinea pigs
Please rather consider working with the RSPCA along their well though-out and extremely carefully considered guidelines and contact them for what you can do in our own area to become an animal friendly school:
https://education.rspca.org.uk/documents/1494931/0/Animal+Friendly+Schools+Guidance+(5).pdf/c7c5fe97-e5a6-fa47-6205-8d22d45cf7c2?t=1558518337650