The job of a fleece garment is twofold. Its main purpose is to provide insulation, and as such a good fleece will be part of most days in the outdoors. The degree of insulation is provided by the pile of the fleece, ranging from a light microfleece through a number of weights, to garments that can only be used in extremely cold conditions. The second purpose is the control of air and moisture flow through the garment. The majority of fleece garments are designed to work as part of a moisture transportation system that starts with first layer or baselayer clothing followed by the breathable fleece garment and maybe a waterproof or windproof shell over that. This keeps the body dry and comfortable when working and when resting.
We have microfleeces, which can be used as a light jumper or a warm thermal base layer, from several sources. They are very soft to touch and feel lovely on. Summer pieces should provide some warmth, but also wick very well to keep you dry and comfortable. Polartec Powerstretch and Pontetorto Technostretch garments are made from a single-sided, stretchy fleece, and are great for providing unrestricted movement when climbing, for example.
For a fleece with a bit more protection from the wind, one might consider the TechFace range from Patagonia, which is available in a variety of styles as well as weights.