You can truncate the date part:
select * from table1 where trunc(field1) = to_date('2012-01-01', 'YYYY-MM-DD')
The trouble with this approach is that any index on field1
wouldn't be used due to the function call.
Alternatively (and more index friendly)
select * from table1
where field1 >= to_timestamp('2012-01-01', 'YYYY-MM-DD')
and field1 < to_timestamp('2012-01-02', 'YYYY-MM-DD')