Not it is available all year round however as it has been a US tradition for hundreds of years this makes it typically more prevalent in stores during the winter months and on the run-up to Christmas.
You will see more of it stacked on shelves and marketed during the Thanksgiving and Christmas holidays - hence why you may believe that it's only available then.
sales have increased typically increase during November and December due to the tradition of drinking Eggnog at Christmas time (holiday season).
Furthermore, Eggnog is a more popular drink in places with cold winter months and another reason why you'll see more people drink this egg yolk drink it in the Northeast United States and Canada than in the south.