IF the front portion of the frame of a 1500 is sufficiently similar to that of a 2500, a Power Wagon's winch mount and winch could be adapted to work but, I rather doubt the frame horns are similar enough. Also, a word of warning- the winch from a Power Wagon is a dealer only item (it is a specialty Warn winch) and is QUITE expensive! The mount is rather pricey as well. If you can find them used for a reasonable price though, they may not be a bad setup to try!
Warn makes a hidden mount kit for the 2002-2005 Ram 1500. But, once again, I don't know how similar the frame horns are so, I don't know how well this would adapt over.
The general consensus in this thread seemed to be that no one makes one for 4th gen 1500s (the first post says it's a hidden mount (the Fab Fours one) BUT, if you Google images of it, it is anything but hidden!!!) :
If you are absolutely fixed on having the mount be hidden- I think your best way to go is likely going to be to make one yourself, or get one fabbed. It wouldn't likely be too hard to make one, just look at other designs from other applications, compare them with the space available behind your bumper, and some up with a design. A winch mount can be VERY simple, just like a tray (look at the mounts that people have used for Jeeps), the complicated thing will be coming up with a beefy way to actually attach it to your frame. Semi-hidden kits (like Fab Fours) and many brushguard kits (like Warn, Ramsey, Westin, etc) tie into the truck's tow hook mounts. It wouldn't be difficult to sandwich the plate of a winch mount between the frame and the two hook and then figure out a couple of other bolt points to utilize as well. I haven't been under a 1500 in years so I can't comment on exactly what points would work. I have seen some winch mounts for other vehicles use (amongst other bolting points) plate sandwiched between the swaybar mount and the frame. The more spread, and the more triangulation that you can get between the mounting points of a well designed plate, the stronger the mounting is going to be!!!