As [wesna] "spring-season" as [osen'] "autumn-season" are equinoxs both. Is it possible to assume that both words were deriving from common root? What are the names of "spring"- and "autumn"-seasons in other Slavic languages?
According to my (Czech) etymological dictionary they are unconnected, "vesna" (spring) derives from indoeuropian *uesr, whereas "jeseň" (autumn) relates to an old-prussian or gothic word for harvest.
As you can see, we have both of those words, but neither is normally used, both are highly poetic and rather new in the language, created artificially during the period of so-called national awakening (around 19th century) based on Polish and Russian equivalents (respectively).
In Polish: wiosna, jesień.
In Ukrainian: весна, осінь (at least my dictionary says so).
bułgarski: (1.1) пролет ż (prolet)
chorwacki: (1.1) proljeće n
czeski: (1.1) jaro ż, książk. poet. vesna ż -> this one is interesting, as a similar word is used in Polish for types of corn which is seeded in spring (zboże jare), as opposed to the types seeded in autumn (zboże ozime)
dolnołużycki: (1.1) nalěśe n, nalěto n
górnołużycki: (1.1) nalěćo n
kaszubski: (1.1) zymk m
rusiński: (1.1) яр ż (jar)
serbski: (1.1) пролеће n (proleće)
słowacki: (1.1) jar ż, książk. poet. vesna ż
słoweński: (1.1) pomlad ż
staro-cerkiewno-słowiański: (1.1) весна / (vesna)
śląski: (1.1) wjosna ż
białoruski: (1.1) восень ż
bułgarski: (1.1) есен ż (this could oppose a Prussian theory)
chorwacki: (1.1) jesen ż
dolnołużycki: (1.1) nazyma ż, nazymje n
kaszubski: (1.1) jeséń
słowacki: (1.1) jeseň ż
słoweński: (1.1) jesen ż
* od prasł. *vesna lub prasł. *vesъna
The word vesna for spring exists in Slovenian (and is also used as a female given name - Vesna), the SSKJ (the official Dictionary of the Slovenian Literary Language) has the word in it. It is, however, archaic and poetic, and everyone says pomlad instead. The word jesen for autumn, on the other hand, is still the common word and is used by everyone.