Perhaps contrary to popular belief, with all of the perspiring and what not... moisture still remains important during the summertime as well. The difference being between summer and winter moisturizers is usually the weight and consistency of moisturizers. This is of course a generalization based on my experience and the fact that I have completely normal skin.
If you have really intense questions about what's best for your skin type...prob best to talk to an expert. I'm big on that--ask the people that know. But I definitely would consider these brands as a good place to start.
Anyway, here are a few of my summer staples (Napoleon Perdis, Supergoop and Kiehls). Oh and the gratuitous NARs plug, love this for pre/post travel. Always. Stay Posh!