It is just a guess, but many Japanese will be busy making preparation for the new year during the time of writing Christmas cards.
これは推測の域を出ないが、クリスマスカードを書く時期には、多くの日本人は、お正月の準備で忙しくしているだろう。
推測の域を出ないが It is just a guess, but
多くの日本人 many Japanese
～で忙しい be busy ~
準備する making preparation
新年 the new year
～の間 during ~
It is just a guess, but many Japanese will be busy making preparation for the new year during the time of writing Christmas cards.
日本 
