I received a few New Year's cards from Japan this year, too. The senders are my friends since high school, college, around when I was 21, and around 25. They all do not do the Internet.
I did not realize Cherry blossoms does not come with the New Year (Santa Clause) in the US until S pointed out.
We describe January "Shin shun" (new spring), especially the first half of January. Spring = Cherry blossoms to Japanese. So, Cherry blossoms on New Year's cards are normal.
This greeting card is for both Christmas and the New Year. Since New Year things are the most important for us, cherry blossoms and the temple are the main characters on this card. But the designer who designed on this card needed to put Santa because this card was meant to be for both Christmas and the New Year.
Santa --> with reindeer --> Santa + reindeer + temple --> Santa in a temple with deer --> Nara (is a very famous Japanese prefecture for the Todai temple which has deers all over around it. There is no cage for them, and they are offensive to get food....)
So, the Buddha in the second picture is called Daibutsu. He is the largest statue of Buddha in Japan who lives in the Todai temple. I used to love to go to see him during my late teens and early twenties. I liked his face. I felt like he knows everything. Well, he is one of the Gods of Buddhism. He should know everything, I guess.
Todai-ji(temple)
I used to have the post cards of him, Nio guardians. I thought he is cool. I thought he has a brother and they are at the gate of the temple protecting enemies trying get in the temple, but maybe the brothers are different guys than I am thinking.
It would be so strange for Americans to see them on a season greeting card. I did not think it's strange because of cultural difference. Funny :)