I plan to continue reading some books I haven't finished during my winter holidays.
I'd like to keep reading some of the books I have started over my Christmas and New Year's holiday.
この場合、次のように言えると思います。
ーI plan to continue reading some books I haven't finished during my winter holidays.
「冬休み中にまだ読み終えていない本を何冊か読み続けるつもりです」
to continue reading で途中まで読んだ本を読み進めるニュアンスです。
books I haven't finished で「まだ読み終えていない本」
ーI'd like to keep reading some of the books I have started over my Christmas and New Year's holiday.
「クリスマス休暇中に、読み始めた本を何冊か読み続けたい」
to keep reading でも「読み進める」ことを表現できます。
books I have started で「読み始めた本」
ご参考まで！
カナダ 
