There are numerous Christmas traditions here. They vary significantly at the different parts of Ukraine.
In most parts of Ukraine on the Christmas Eve people create so-called ‘Vertep’ (means cave in ancient Greek). These are scenes from Bible of Jesus birth. They show little Jesus in manger, Mary, strangers offering their gifts and Bethlehem star in the sky. Those verteps are exhibited at public places, usually near or inside churches. At night candles are installed inside verteps for people who come to church for the night service can observe them.
The Christmas Eve is called in Ukraine ‘Sviaty Vechir’ (Holy Evening) sometimes also called ‘Sviata Vecheria’ (Holy Supper). People usually cook some tasty foods for this evening. There should be at least 12 different foods on the table. Those should mandatory include ‘Kutia’ -- the ritual food which is prepared from cooked wheat and special syrup containing diluted honey, grated poppy seeds, raisins and sometimes walnuts.
St. Nicolas (Santa Claus) also called here ‘Did Moroz’ is an ubiquitous Christmas character and is supposed to bring some gifts under the Christmas tree this night.
Also in some regions people make decorated Christmas eggs very similar to Easter eggs -- ‘Pysanky’.
Halloween is not celebrated in Ukraine but some similar traditions are performed here for Christmas. Children this evening come around their neighbors with torches and sparclers (called here Bengal lights) spreading grains and colored seeds. They wish people good health and abundant harvest for the next year and ask for some donations. Also they perform some Christmas songs called in different parts of Ukraine ‘Koliadky’ or ‘Shchedrivky’ like these:
"Radujsia zemle, radujsia. Syn Bozhyj narodyvsia." -- Joy, Earth, Joy. The Son of God was born.
"Dobryj vechir, Sviaty vechir. Dobrym liudiam na zdorovja." -- Good evening, Holy evening. To good people for good health.