If you are leaving the pigs outside unattended you need a secure run, both of my groups have enclosed wooden runs as we have cats, foxes and plenty of birdlife around that could attack the piggies while they enjoy some outside fresh air. If you are going to stay outside with them all times when they are in the run, a wire one is fine, but be aware people have in the past posted that birds of prey have attacked their pigs in open topped runs.
Its irrelevant if they get to have grass time or patio time as long as they have something to eat and shelter while outside, the fresh air and different environment will be great for them. In the winter if you are able, an inside set up run would be fine but not imperative as I cannot do this myself having a dog that would not play nicely with my pigs either.
And on that subject, if you are able to keep the dog and pigs separate, ensure safety measures are in place just incase (I have a stairgate on the pigs room door and a fence around the hutch outside), my dog is respectful to them in their hutch, pens and runs but was a working lurcher in her past so was used for catching rabbits and I respect that part of her so I make sure I do everything possible to keep both sides happy. I do have lap time with my pair of boys and she has learnt that when they are with me, they are to be given space and not to be touched, it would be a different matter should they get away from me and this is why I am very careful, however it is possible to manage both.
And you really do need a 120 or larger cage when possible, the size you have is far too small and they will grow quickly, it would be better for them to have the space they deserve.