I spent the winter/ winter in Austria.> Both are acceptable . The winter > you are specifying the season of winter Winter > you just specifying winter as a noun But , if you want to specify a certain winter , then the article should be used . In the winter of 2015 , I was in Austria

"I spent the winter in Austria" sounds natural. I wouldn't say, "I spent winter in Austria" (doesn't sound correct). "Winter is a time for hot cocoa and blankets" (noun: without the article)