You should probably use exists since you aren't really needing a count of anything.
You don't indicate how you want to consume the results of multiple counts, however one thing you could do is use concat to return a list of the columns meeting your criteria:
The following sample table has 5 columns, 3 of which have a value on at least 1 row.
create table t (col1 int, col2 int, col3 int, col4 int, col5 int)
insert into t select null,null,null,null,null
insert into t select null,2,null,null,null
insert into t select null,null,null,null,5
insert into t select null,null,null,null,6
insert into t select null,4,null,null,null
insert into t select null,6,7,null,null
You can name the result of each case expression and concatenate, only the columns that have a non-null value are included as concat ignores nulls returned by the case expressions.
select Concat_ws(', ',
case when exists (select * from t where col1 is not null) then 'col1' end,
case when exists (select * from t where col2 is not null) then 'col2' end,
case when exists (select * from t where col3 is not null) then 'col3' end,
case when exists (select * from t where col4 is not null) then 'col4' end,
case when exists (select * from t where col5 is not null) then 'col5' end)
Result:
col2, col3, col5