The correct syntax depends on how the field is stored in the database and how cast() could transform it and the variable-values whereby the easiest approach is to keep it simple and to try to use the same formats. Quite often a date is stored as a number like 42874 for today - then you could use: let var = num(date#('03222015', 'MMDDYYYY')); to set the variable and you would be able to make a very simple where-clause, like: where FIELD_DATE >= $(var).
Another way to simplify such where-conditions could be to apply them on a preceeding load, like:
load * where FIELD_DATE >= $(var);
select * from ...
on which you could use qlikview-functions to determine your conditions. Of course this is only practically if the sql-load respectively their run-time is relative small because the whole sql-table will be queried on this way.