The horsetails (Order Equisetales, Class Polypodiopsida) comprise 15 species known at the present day, all in the genus Equisetum (Encyclopaedia Britannica). However, they have a substantial fossil record.

The stem-group part of the phylogeny published by Elgorriaga et al (2018) is represented by the following time tree:
​Figure 1. Time tree of the stem-Equisetales
​This tree indicates that the most basal stem-Equisetales are represented by the polytomy comprising Peltotheca furcata and two species of Protocalamostachys. 

Two fossil horsetails have been identified as the oldest members of the stem group:
  1. Hamatophyton verticillatum, described from various formations of Late Devonian (Famennian) age in Jiangsu, Hunan and Anhui Provinces, China (Wang et al, 2005; Elgorriaga et al, 2018);
  2. Rotafolia songziensis, described from the Late Devonian (Famennian) Xiejingsi Formation in the Huangkuang section, Liujiachang town, c. 30 km south-west of Songzi City, south-western Hubei Province, China (Wang et al, 2005; Elgorriaga et al, 2018).
Unfortunately, no public-domain images are available of these species. Furthermore, the public domain contains relatively few such images for the other species shown in the above tree. Those that are available are shown below (click on image for a larger view):
Figure 2. Images of stem-​Equisetales
The above images are ordered from most basal to most crownward, but there are too few of them and they do not provide the consistent fields of view necessary to allow evolutionary trends to be suggested.  

With respect to the crown group, the full tree presented by Elgorriaga et al (2018) indicates that the oldest member of the crown-Equisetales is Equisetum dimorphum, of Early Jurassic age. However, in the phylogenetic tree published in the following year by Clark et al (2019) this species is not shown unambiguously to belong to the crown group. In the latter tree, the oldest crown horsetail is Equisetum fluviatoides, which we accept as a conservative interpretation here. This fossil was found in the Paleocene Ravenscrag Formation in Saskatchewan, Canada (McIver and Basinger, 1989). Again, no image is available in the public domain.

As indicated in Figure 1, the horsetail stem-to-crown transition took place over a long period of between 293 and 316 million years, from Late Devonian to Paleocene time.

References

Clark, J. W., Puttick, M. N., & Donoghue, P. C. (2019). Origin of horsetails and the role of whole-genome duplication in plant macroevolution. Proceedings of the Royal Society B, 286(1914), 20191662.

Elgorriaga, A., Escapa, I. H., Rothwell, G. W., Tomescu, A. M., & Rubén Cúneo, N. (2018). Origin of Equisetum: Evolution of horsetails (Equisetales) within the major euphyllophyte clade Sphenopsida. American Journal of Botany, 105(8), 1286-1303.

McIver, E. E., & Basinger, J. F. (1989). The morphology and relationships of Equisetum fluviatoides sp. nov. from the Paleocene Ravenscrag Formation of Saskatchewan, Canada. Canadian Journal of Botany, 67(10), 2937-2943.

Wang, D. M., Hao, S. G., & Wang, Q. (2005). Rotafolia songziensis gen. et comb. nov., a sphenopsid from the Late Devonian of Hubei, China. Botanical Journal of the Linnean Society, 148(1), 21-37.
Image credits – stem-Equisetales
  • Header (Western Scouringrush - Equisetum hyemale subsp. affine – photographed near Augusta, Missouri, USA): Allen Gathman, CC BY-SA 2.0 <https://creativecommons.org/licenses/by-sa/2.0>, via Wikimedia Commons 
  • Figure 2 (Peltotheca furcata): From Open Access article Tomescu, A. M., & Rothwell, G. W. (2022). Fossils and plant evolution: structural fingerprints and modularity in the evo-devo paradigm. EvoDevo, 13(1), 1-19. 
  • Figure 2 (Protocalamostachys arranensis): From Open Access article Bateman, R. M., Stevens, L. G., & Hilton, J. (2016). Stratigraphy, palaeoenvironments and palaeoecology of the Loch Humphrey Burn lagerstätte and other Mississippian palaeobotanical localities of the Kilpatrick Hills, southwest Scotland. PeerJ, 4, e1700. 
  • Figure 2 (Cruciaetheca sp.): From Open Access article Tomescu, A. M., & Rothwell, G. W. (2022). Fossils and plant evolution: structural fingerprints and modularity in the evo-devo paradigm. EvoDevo, 13(1), 1-19. 
  • Figure 2 (Palaeostachya sp.): Ghedoghedo, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons
  • Figure 2 (Calamostachys binneyana): Botanical Society of America, licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
  • Figure 2 (Calamostachys tuberculata): Daderot, CC0, via Wikimedia Commons
  • Figure 2 (Neocalamites sp.): Hans Hagdorn, licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License
  • Figure 2 (Equisetites arenaceus): Hans Hagdorn, licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License