This paper proves that all power series over a maximal ordered Cauchy complete non-Archimedean field satisfy the intermediate value theorem on every closed interval. Hensel's lemma for restricted power series is the main tool of the proof.
"Hensel's lemma and the intermediate value theorem over a non-Archimedean field." J. Commut. Algebra 9 (2) 185 - 211, 2017. https://doi.org/10.1216/JCA-2017-9-2-185