A spell or ability that counters spells can still target your spells after Veil of Summer resolves. When that spell or ability resolves, your spell won't be countered, but any additional effects of the countering spell or ability will still happen.

If your opponents have cast more than one blue or black spell, you still draw only one card as Veil of Summer resolves.

Veil of Summer has no effect until it resolves. It can be countered.