How do horsetails reproduce without seeds or flowers?

Horsetails (Equisetum) reproduce through an alternation of generations, involving an asexual sporophyte phase and a sexual gametophyte phase. Because they are homosporous, they do not produce seeds or flowers.1

The Reproductive Process

• Spore Production: The sporophyte (the visible horsetail plant) produces strobili (cones) at the tips of its shoots. These cones contain sporangiophores, which bear sporangia that release large numbers of spores.21
• Dispersal: Each spore features four ribbon-like appendages called elaters. These coil and uncoil in response to humidity, which helps the spores disperse.21
• Gametophyte Development: Upon landing in a suitable environment, spores germinate into small, green, pincushion-like gametophytes. These produce antheridia (sperm-producing organs) and archegonia (egg-producing organs).21
• Fertilization: Sperm swim to the archegonium to fertilize the egg, forming a zygote that develops into a new sporophyte.1

While this sexual cycle exists, horsetails also rely heavily on vegetative reproduction to survive in nature.1