Create a .dir-locals.el file in the directory of interest, with the following contents:
((dired-mode . ((dired-omit-files . "\\.html\\'"))))
If you want to omit the usual suspects as well, then use this regexp (which is the OR of the standard value with the html value above):
Visiting the ...
dired-omit-mode, as currently defined, looks only at the (relative) file name. It does not look at the permission bits.
You would need to define a mode that (1) does first what dired-omit-mode does - match file names and omit them, and (2) then matches the x permission bits at the beginning of the file line.
The second is a separate operation because dired-...