Whenever you wonder whether a spell’s effects can be dispelled or suspended, you need to answer one question: is the spell’s duration instantaneous? If the answer is yes, there is nothing to dispel or suspend. Here’s why: the effects of an instantaneous spell are brought into being by magic, but the effects aren’t sustained by magic (see PH, 203). The magic flares for a split second and then vanishes. For example, the instantaneous spell animate dead harnesses magical energy to turn a corpse or a pile of bones into an undead creature. That necromantic magic is present for an instant and is then gone. The resulting undead now exists without the magic’s help. Casting dispel magic on the creature can’t end its mockery of life, and the undead can wander into an antimagic field with no adverse effect.
Another example: cure wounds instantaneously restores hit points to a creature. Because the spell’s duration is instantaneous, the restoration can’t be later dispelled. And you don’t suddenly lose hit points if you step into an antimagic field!
In contrast, a spell like conjure woodland beings has a non-instantaneous duration, which means its creations can be ended by dispel magic and they temporarily disappear within an antimagic field.