4'x2' is really minimal space for adults especially boars .
Have you seen the sizes of some 'Breeders Cages' though , they are inhumane . I know its a Mum+ babies so technically don't need tonnes of space , but they're stacked 5 high. What a grim life 
Conservatory sounds fine - in winter you can insulate .
C&C are better than a hutch though. You need to line the floor ( I use cardboard because I'm too tight fisted to buy the proper lining ) .
the grids I have are 14" squares and they've never attempted to jump out .
You can use cardboard or carpet to insulate the sides , lots of hay to snuggle . Snuggle pads ( solid plastic heat discs that you microwave)
My 2 piggies have a C&C in the small bedroom for winter. The radiator is off in that room, but there's no door . They are next to DH/me (so I hear them whittering at 3am) and DD is always in her room and scoops them up to cuddle.
Their cage is 70" x 42" . all one level, with a covered hay area. They have a tunnel, we give them cardboard boxes to explore .
We have a wooden playhouse for summer but these pigs are in 24/7 for winter because they're getting on a bit .
Guinea=pigs don't cope with damp, draughts or changes in temperature.
You need to protect them from direct sun, over heating, other animals.
Chemicals like sprays, detergents(if you use fleece)
Sudden noise (though they tend to ignore most house hold noise and use their finely tuned hearing for the fridge door)
They are wonderful little animals . I kept pigs as a child and my DD and I have kept pigs since she was 9yo (she's 16 now) .
We got DD boars from rescue (GP1 and GP2) and it just spiralled from there.
Try and find out their history . Most guinea-pigs end up in Rescue through no fault of their own (mostly allergies or 'Kids got bored' )
They might take a while to settle into a new house but you'll win them round with Food+Routine+Routine based round food.
If you're late feeding them , they'll tell you 
Only one of mine has been unsuitable as a childs pet , not a biter but a gnawer, though as an adult it didn't bother me , a child would say "It bit me...."