I can not find any apps in the store that will open .mht files. Doesn't mean there are none, just that my quick search didn't turn up any.
There appear to be a couple that will open .eml files. Just go to the App Store and search for .eml. I can't offer any advice on how well they will work.
Once you have an app that will open the file type, you find that the arrow you tried in DropBox will (should) list the compatible app, and allow you to open it there.
Your other option is to convert the files before you try importing them into the iPad.
If you are using Windows I believe there are several free or cheap programs that will convert anything you can print to a PDF. I don't much care for cutePDF myself, but it is the only one I can remember and it does work, if not always the way you expect.
In OS X, this is built in.
There are a multitude of apps for the iPad that will read PDF files. iBooks is free, and makes a good pdf reader. GoodReader is a decent reader, does much much more, and can be set up to upload/download directly from DropBox.