Instead of

date 'TODAY()'

use

date '"&TEXT(TODAY(), "yyyy-mm-dd")&"'"

NOTES:

• The last " should be placed in a proper place in order to have a text value as the second argument of QUERY.
• 'TODAY()' doesn't returns Today's date, it returns a string with the word TODAY followed by parenthesis.

Try this

=ARRAYFORMULA(QUERY({A3:H, HOUR(A3:A)}, 
 "select Col7,sum(Col3),sum(Col5),sum(Col8) 
 where Col1 is not null and Col9=7 
 and Col1 = '"&TEXT(TODAY(), "yyyy-mm-dd")&"' 
 and Col1 = '"&TEXT(TODAY() + 1, "yyyy-mm-dd")&"' 
 group by Col7 
 label sum(Col3)'',sum(Col5)'',sum(Col8)''", 0))​​

Related

• Querying for the last results with group by

Instead of

date 'TODAY()'

use

date '"&TEXT(TODAY(), "yyyy-mm-dd")&"'"

NOTES:

• The last " should be placed in a proper place in order to have a text value as the second argument of QUERY.
• 'TODAY()' doesn't returns Today's date, it returns a string with the word TODAY followed by parenthesis.

Try this

=ARRAYFORMULA(QUERY({A3:H, HOUR(A3:A)}, 
 "select Col7,sum(Col3),sum(Col5),sum(Col8) 
 where Col1 is not null and Col9=7 
 and Col1 = '"&TEXT(TODAY(), "yyyy-mm-dd")&"' 
 and Col1 = '"&TEXT(TODAY() + 1, "yyyy-mm-dd")&"' 
 group by Col7 
 label sum(Col3)'',sum(Col5)'',sum(Col8)''", 0))​​

Related

• Dynamic date range query
• QUERY most recent date prior to today
• Querying for the last results with group by