No judgement, it's hard to know some times. May I ask how old your daddy boar was? I wonder if it's possible that he had a deformity, such as a heart condition or some other 'ticking time bomb' type anomally that he passed on to his babies? May I ask if he has sired babies before, and if they all thrived? Not asking in order to judge, but wondering if genetics are playing a part.
May I also ask how long you have had your piggies in this set up? I ask because if you have kept them like this for over a year they have already been through the changes of the seasons, humidity and temperature without issues then I wouldn't have thought that their environment would be the major factor, unless something has developed over time within the shed, such as a fungal/mould or damp issue. These are not always easy to spot.
My guess would be on something contagious, sadly. Possibilities include viruses, infections etc, but I also would like to ask if you have any wild animals visiting your garden, or if there is any sign of rodent damage to your shed? Contaminated grass or urine/droppings from rats or mice may harbour bacteria or parasites that your pigs perhaps could have picked up.
It's good to check on the shed for draughts, as you say. Draughts can increase the likelihood of illness, but I wonder if that's not the case if you have had this set-up for some time without issues.
If possible it may be worth considering trying to house them indoors temporarily in order for the temperature to stay constant (which is likely to be of help to any who are falling ill, and for those that may require treatment), plus you are perhaps more likely to pick up on any early signs, such as sneezing, changes in behaviour, listlessness, signs of pain, a change in eating habits or anything else which doesn't seem quite right.
If you cannot temporarily bring them all inside then it would be worth investing in a pen or cage for quarantine purposes to isolate any from the moment you suspect that they/it is ill.
Getting them all checked out with a vet is a very sensible precaution. I wonder if it would be easier to book a vet to make a home visit?
Sadly when a piggy starts to lose weight it becomes an urgent matter and such a piggy cannot afford to wait a few days. Again this is not judgement at all, many people don't realise how urgent the situation is, and in an ideal world we would all be able to drop our other commitments and go straight down the vets. I know it can be hard to do, but sadly losing weight is very often an emergency situation. When a guinea pig stops eating their guts can slow right down or even stop completely. This can actually be deadly very quickly, not through starvation, but because the guts can actually shut down, causing a downward spiral of bloat and other issues.
The loss of fur may indicate mites or a fungal infection, amongst other things. A mite infestation can get bad quite quickly on a guinea pig, and if left untreated can cause death through blood loss and infection. babies succumb faster. Mites are in piggies in low levels and are generally not an issue at all, but stress (either emotional physical) can cause a drop in the immune system which allows the mites to breed out of control. If mites have been a factor it may mean that there was another issue, possibly a health issue to start with, and the mites just being a secondary factor in the guinea pigs's death. The good news is that mites are unlikely to spread to the others, especially if they are healthy and happy. The other good news is that mites are usually easily dealt with by a course of ivermectin injections from the vet. Mites would need to be diagnosed by the vet though in the first place, as I say there are several causes of hair-loss.
I really think it is worth keeping your vets appointment and discussing all of this. It may also be worth, if you still are able to, taking along the body of one of the pigs for post-mortem.
