SQL> SELECT * FROM test;

MENO            DEN_A_MESIAC_NA
--------------- ---------------
Jozko           29.12
Ferko           2.1

SQL> SELECT * FROM test
  2  WHERE to_date(den_a_mesiac_nar, 'DD.MM') BETWEEN to_date('28.12.2015', 'DD.MM.YYYY') AND to_date('4.1.2016', 'DD.MM.YYYY')
  3  OR add_months(to_date(den_a_mesiac_nar, 'DD.MM'), 12) BETWEEN to_date('28.12.2015', 'DD.MM.YYYY') AND to_date('4.1.2016',  DD.MM.YYYY');

MENO            DEN_A_MESIAC_NA
--------------- ---------------
Jozko           29.12
Ferko           2.1