Over summertime you need not worry too much about the weather in Iceland. It will rain, it will shine but harsh winds or conditions over june, july or august are exceptions.
A viking saying goes along the lines of “no one is worse for wear if wet” and this is true. But what many visitors to Iceland forget is that nights in Iceland, even in high summer, can get pretty cool. Cool as in one or two degrees celcius.
Thus, you have to make sure if you are exposed to the elements to keep extra clothes handy at all times. Especially if you stay in a tent or hitchike around the country.
For detailed information about weather conditions check out the local weather office, Vedurstofan, and expecially before heading into the highlands. That can mean the difference between life and death.