Sanjay G. ,sorry but what u posted is definitely wrong.
The format in the TO_DATE has nothing to deal with the format of the string at the right side of the greater operator.
yxez, pls post here the results of
show parameter nls
also try
....
where to_date(birthdate,'mmddyyyy')>=to_date('01.01.1990','dd.mm.yyyy')
and let us know if it works

Regards
Boris