I think the definite article before a season is acceptable in many situations. It can't be considered wrong in general.
Here are some phrases I could find in just one book, "The Shining", by Stephen King:
"In the winter the road was closed... "
"... they could have passed the winter quite nicely..."
"So far the fall had been almost preternaturally beautiful."
"They were together again in the spring and ... "
Here's an interesting discussion on this subject:
Obrigada, damarx! É por isso que eu escolhei 'seguir' você. Continuo aprendendo aqui-- as duas línguas!
Obrigado, emeyr! Português é minha língua nativa, mas estou aprendendo inglês aqui também
"Spring will be here soon" was not accepted, but suggested "will begin" as a correct translation? Chegar has always (so far) been shown and used as "arrive." I understand how BEGIN is also proper in common speech, but that wouldn't have been my choice of words within a lesson here.