I made columns that simply lists all the schools for each student under a date column header. I only need to count the schools - I don't want to see any student data. I have a form that needs to be submitted to the state and there is a cell with the date we are submitting. I want to use an IMPORTRANGE to go to the other spreadsheet and find the column where the date matches the form date and pull back the count of schools in that column. I tried using INDEX/MATCH, etc., and while I have those working on the form for other data already on my spreadsheet - I can't seem to get them to work on the 'outside' spreadsheet. Any help is appreciated! I'm attaching an example spreadsheet with more explanation. I hope it's clear. Thank you.
ztiaa has provided a good solution. I will suggest another which pivots the data differently. I feel that having the dates go across columns is going to quickly become unwieldy. So this approach leaves the dates running down the right side with the schools running as column headers. My solution also includes exceptions such as snow days, as those will likely be important to see at a glance as well. Just be careful to use the same notation for such exceptions. For instance, always use "snowday" (not, eg., "snow day") or "prep day" (not, e.g., "prep").
In Sheet1, use IMPORTRANGE to bring in the data exactly as you have it listed in your sample sheet (i.e., dates at top, school names or exceptions under each date header).
Then, in a new sheet, place the following formula in cell A1:
=ArrayFormula({QUERY(SPLIT(FLATTEN(FILTER(Sheet1!1:1&"~"&INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!1:1<>"")),"~",1,0),"Select Col1, COUNT(Col1) WHERE Col2 Is Not Null GROUP BY Col1 PIVOT Col2 FORMAT Col1 'mmm dd'"),TRANSPOSE({"District Totals",MMULT(SEQUENCE(1,ROWS(Sheet1!A2:A),1,0),IF(FILTER(INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!1:1<>"")="",0,1))})})
This assumes that the first sheet is, in fact, named Sheet1. If it is not, you'll need to change every instance of that sheet name in the formula.
It will probably further aid visual ease if you freeze Row 1 and Column 1 (View > Freeze > 1 row / 1 column).
ADDENDUM (after seeing realistic copy of OP's sheet)
=ArrayFormula({TRANSPOSE(QUERY(SPLIT(FLATTEN(FILTER(Sheet1!1:1&"~"&INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")),"~",1,0),"Select Col1, COUNT(Col1) WHERE Col2 Is Not Null GROUP BY Col1 PIVOT Col2 FORMAT Col1 'mmm dd'"));{"District Totals",MMULT(SEQUENCE(1,ROWS(Sheet1!A2:A),1,0),IF(FILTER(INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")<>"",1,0))}})
If you prefer to see the name of the exception (e.g., "snowday") rather than the count of 1 for each exception in the "District totals" line:
=ArrayFormula({TRANSPOSE(QUERY(SPLIT(FLATTEN(FILTER(Sheet1!1:1&"~"&INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")),"~",1,0),"Select Col1, COUNT(Col1) WHERE Col2 Is Not Null GROUP BY Col1 PIVOT Col2 FORMAT Col1 'mmm dd'"));{"District Totals",IF(MMULT(SEQUENCE(1,ROWS(Sheet1!A2:A),1,0),IF(FILTER(INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")<>"",1,0))=1,FILTER(Sheet1!2:2,Sheet1!2:2<>""),MMULT(SEQUENCE(1,ROWS(Sheet1!A2:A),1,0),IF(FILTER(INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")<>"",1,0)))}})
If you want exceptions (e.g., "snowday") to always appear at the bottom instead of in alphabetical order within the school-name list:
=ArrayFormula({TRANSPOSE(QUERY(SPLIT(FLATTEN(FILTER(Sheet1!1:1&"~"&IF(REGEXMATCH(UPPER(INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A))),INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A))),,"‡")&INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")),"~",1,0),"Select Col1, COUNT(Col1) WHERE Col2 Is Not Null AND Col2 <> '‡' GROUP BY Col1 PIVOT Col2 FORMAT Col1 'mmm dd'"));{"District Totals",IF(MMULT(SEQUENCE(1,ROWS(Sheet1!A2:A),1,0),IF(FILTER(INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")<>"",1,0))=1,FILTER(Sheet1!2:2,Sheet1!2:2<>""),MMULT(SEQUENCE(1,ROWS(Sheet1!A2:A),1,0),IF(FILTER(INDIRECT("Sheet1!2:"&ROWS(Sheet1!A:A)),Sheet1!2:2<>"")<>"",1,0)))}})