Go to View-Options (or press O), then Output.
Select one of the two options under DirectShow Video indicated in the image below:
Apply, then open the DVD and add the subtitle – even drag and drop works.
Chances are that the subs you find are not synced – but for that MPC-HC can help, as shown in this answer..
I have found this answer here.
PotPlayer and KMPlayer are both able to accomplish this right away (I would recommend the first, which looks to me like a non-bloated fork of the second.)
DrakaSAN gave an answer saying that VLC also plays DVD with external subs, but after more testing, the VLC solution seems very unstable, it sometimes does not work for parts of the video, and especially subs disappear after seeking back or forth. I keep it here for reference and in view of further findings.
BSPlayer PRO seems to be able to accomplish the task.
A different approach (useful with a player that cannot play external subs with DVDs) is to display the subtitles over the video with a separate specialized program, like Greenfish Subtitle Player. Of course, this works with any playing video, not just DVD.
As far as I know some players, for example Media Player Classic Home Cinema support this, although I’ve never tried it. In the file menu you’ll find a “Subtitle Database”, which might be the function you’re looking for.
VLC do that, you just have to drag’n drop the subtitle file while the dvd is playing, or opening it via the menu. (Subtitles>Add subtitles or something like that).
AS SAID BY CIPRICUS.
This method does work with DVD, but the video output need to be changed to OpenGL.