Do you want a batch to do the work for you?
Then to design a batch you have to decide ALL of the variations you want
to include: How many different days, source directories, and destination
directories. Will a change of year or month cause a problem?
Depending on desires one can then use menu choices like I showed or
batch command input variables like %1 %2 %3.
FORFILES might also be a good command to use.
If the only variable is date then start your batch with _MoveBat %1
where %1 is the MMDD you want.
_MoveBat
---------------
DEL c:\todayhtr\*.* /q
COPY c:\htr\%1*.* C:\todayhtr\
PS: I think you have a typo here
set filestocopy=c:htr\\%DATE:~4,2%%DATE:~7,2%*.*
^^ ^^