First thing - caulk around the frame. That will help a little bit
What about making a winter coat for the glass? Pick a fabric you love, line it with off-white and insert batting between face fabric and liner. Make sure it is at least 1" bigger on each side to help keep the cold out. Attach it to the door over the glass using Velcro or snap tape. You can remove it during warmer months.

Do you have a storm door in front of it? With a low profile frame? We have a front door from the 1920's with some leaded glass inserts that do let in the cold in midwestern winters, but a good quality storm door has improved that quite a lot without detracting from the beauty of the old wood door.

Thank u for the helpful tips!

What kind of caulk should I use?

missmiffy - Go to your local hardware store and they can recommend the appropriate type of caulk.