With grep:
cat *.log | grep -vc '^.\{301\}'
To match lines with length <=300 we grep with -v (invert match) for any 301 characters, as the search pattern is limited to one line for grep. Pattern is anchored at the beginning of the line with ^. And -c counts the matching lines.
If you want to have some basic progress indicator, you can use pv from package moreutils:
pv *.log | grep -vc '^.\{301\}'