So here are some suggestions for seasonal flowers. Names of flowers correspond with pictures, left-right and top-bottom.
Spring: tulips, ranunculus, sweet peas, heather, iris, peonies (late spring- early summer), hyacinth, ranunculus again, peonies again, lilacs
Tulips you can usually get year-round, but you'll probably get a better price in the spring. Many of these others just aren't available when they're not in season.
*sweet pea and pink peony pictures from countryliving.com
Summer: bright summer mix (lilies, mums, asters, etc.), roses (although you can get them any time), delphinium, cornflower, lilies, lisianthus, chrysanthemums, alstroemeria, stock (late spring- early summer), chrysanthemums (fuji mums), asters, sunflowers (late summer)
Fall: dahlias, chrysanthemums (pom-pom and fuji), sunflowers, dahlias again, sunflowers again, scabiosa pods, asters, chrysanthemums again.
Dried flowers or foliage are also commonly used in fall arrangements.
*red dahlia boutonniere and orange dahlia bouquets from theknot.com
Winter: amaryllis, sweet peas (late winter), anemones (though really, these are available most of the year except the middle of summer), green holly, poinsettias, camellias, red holly berries, pine/cedar greens
Winter weddings don't just have to be Christmasy! :)
*green holly boutonniere from theknot.com
While this list is by no means comprehensive, it does include a lot of my favorites, and a lot of the more popular choices. Not surprisingly, summer is when the most flowers are in season, so you'll have the greatest variety to choose from. But you're definitely not limited to just roses or carnations other times of the year. And if you're looking to save a bit, try to go with something that's in season!