Yes, we can. We typically use "the" to indicate a particular season (e.g., the summer of 1985, the winter of the big snowstorm, etc.). But we can also say, "I'll be going to Italy in the spring" if it's clear that you mean the upcoming spring.

Hopefully, I will be able to answer this question before summer. If not, then perhaps before next autumn or before spring of 2015. :P

Yes, you are using it correctly. :)

In a phrase of time we often use a singular noun without an article: in winter/summer/autumn/spring But the noun takes a/an or the if there is an adjective before the noun or if there is a phrase or clause after it: The winter when we had all that snow. in the summer of 2005 The summer house was a simple wooden construction.