Almost yes. (You've used the wrong preposition in your second sentence.)
This first sentence is fine as-is:
His music always brings me back to last winter.
Here is another example usage of that construct, taken from a college newspaper:
This song brings me back to the winter of my senior year of high school, just a few months before I was going to graduate.
As for your second sentence, change the in to of and it sounds just fine:
His music always brings memories of last winter back.
We typically have memories of something, not memories in something. Here is a quote by the musician Bob Marley:
The things that seem insignificant to most people such as a note, song or walk become invaluable treasures kept safe in your heart to cherish forever. Memories of your childhood come back and are so clear and vivid it’s like being young again.