Insulation, Radiant and Vapor Barriers - insulating for slab foundations

I have purchased a new home that has a slab foundation
in the bedrooms.
I am looking for ways to insulate under the carpets
to keep them warmer and to save money.

They should have put insulation there at the slab edge when it was built. Lots of time you can go around the footing there and put insulation board next to it this helps. Or put the best rug pad you can under the rugs. ED;)

The following is an exert from the above mentioned website;

Insulation may be applied on top of an existing slab in this way (from top to bottom):

Finish flooring
Rosin paper
Subflooring
Rigid foam insulation laid between moisture resistant furring strips that are attached to the concrete
A layer of 6 mil [0.006 inch (0.15 mm) ] polyethylene plastic as a moisture retarder.

An alternative is to make a "floating floor." This consists of (from top to bottom):

Finish wooden flooring (top)
Rosin paper
Two layers of half inch OSB or plywood screwed together, overlap all seams by several feet, hold the edge of the wood back from the walls by half an inch, to be the subflooring
Rigid foam board insulation without the furring strips (as in the last example).
The above methods have the following advantages and disadvantages.

Advantages:

It's a relatively simple installation for retrofit work.
It thermally isolates the floor from the earth below.
The floor surface is approximately the ambient interior air temperature and more comfortable to stand on than concrete.

Disadvantages:

The foamboard requires a fire-rated covering.
It may increase frost depth around the slab edge in extreme climates.
In the summer, it separates the space above from the cooler earth.
There is a loss of about 2 inches (51 mm) of head room.

I once lived in a rental, built on a slab, pad & carpet, floor always miserably cold in the winter, I carefully pulled up the baseboards, caulked the seam between the sill plate & the slab with lap & gutter caulk & reinstalled the baseboards, I thought it helped out alot, but did have to repaint the trim. My $.02 for what it's worth. ;)

does a radiant barrier work in this situation? For NJ? Not concerned about cooler earth in summer.