Actually, they can both summon and attack with magic.
1) Summon 4 air elementals.
2) Attack with a fireball.
Note: all of this happens after casting antimagic.
Antimagic prevents targeting a spell on a creature, but the creature itself can still cast spells.
Antimagic is only disadvantageous on a hero because (if I'm not mistaken) it removes their Potion of Immortality.
So, after casting antimagic on a hero, can they still cast spells? But this is probably in Equilibris, because in Warriors of the Whirlwind and Tempest, antimagic definitely prevents a hero from casting any spells in battle. And phoenixes, if antimagic is cast on them, will not be able to resurrect. If this was fixed in Equilibris and everything is as you say, then that's great! I have another question about summoning. Let's say a druid summons creatures and then casts antimagic on them. Can they then replenish this group of creatures by summoning more? I don't remember.