I've had much success saving and reseeding spent blooms from cosmos plants year to year and was wondering if it is possible to do the same with zinnia blooms. If so, how do I single out the seeds as they are not as visible as on the cosmos.

To save the seed, just take care to pull off the heads as they fade. This is known as "deadheading," but instead of tossing the spent blooms, examine them to see if they house viable seed. If you pull the heads too early, the bees, Mother Nature, and other pollinators may not have had the chance to do their work, and the seed won't be ready. The flower head on zinnias is ready when they make a distinctive "POP" as you snap them off. The seed is inside the cone, just behind the petals. In fact, follow the petals to the seed at its base.
Test the flower's seed to make sure it's ready, even before you pick it, by peeling back the petal until the seed's exposed. It should be green or brown (if very dry) but NOT white or light colored. Let the heads dry thoroughly for several days before putting them in a paper bag. The paper will absorb any excess moisture as the heads over-winter. Then put the paper bag in a large plastic bag to extra insurance. The goal is to store them in a cool, dry place all winter.
Seeds from hybrid plants won't yield the exact same kind of plant, producing instead a genetic mix of traits from both parent plants in a very random assortment - even bordering on bizarre. There will be no predicting what you'll get! Open pollinated varieties are best for generational consistency. And only stringent greenhouse controlled conditions will produce near exact copies of flowers. Spacing flowers in the garden has everything to do with color integrity. Even a neighbor's flowers can work their way into your beds, thanks to the pollinators and the wind and other conditions.
The seed's greatest enemies are moisture and heat; so be sure to store your treasures in a cool, dry place. No need to refrigerate zinnia seeds. Just keep them dry and cool over the winter. Keeping the thoroughly dried seeds in an air-tight coffee can or plastic container extends the life of the seed by preserving the water inside of it, The water is needed to nourish first growth and burst the seed from the pod in the soil in spring.
Info from Van Dyke Farms….