Here's an example where I've already converted the dates to MMDD
SQL> create table t ( d varchar2(10), lo varchar2(10), hi varchar2(10));
Table created.
SQL>
SQL> insert into t values ('0224','0131','0313');
1 row created.
SQL> insert into t values ('0224','1131','0313');
1 row created.
SQL> insert into t values ('0224','0615','0913');
1 row created.
SQL>
SQL> select *
2 from t
3 where ( lo < hi and d between lo and hi )
4 or ( lo > hi and ( d between lo and '1231' or d between '0101' and hi ) );
D LO HI
---------- ---------- ----------
0224 0131 0313
0224 1131 0313