Yes, but it's a tad more complicated to explain.
Open the finder by clicking the icon in the dock.. go to a random folder; "Movies" in this example. From here, stretch the finder window to the size you'd like.
Once you've got a decent size, backtrack out of the folder by pressing back /level up until you get back to the user home folder (default location when you open finder); now close Finder.
If you now open finder from the dock it should remember that previous size.. however, if you open the HD drive icon from the desktop then it might show a smaller finder window, to get around this simply navigate to the HDD when backtracking and it will set a size to remember.