Definitely use a 00 steel wool; 4/0 is just for rubbing out final finishes.
Any chemical stripper will work optimally at 85 degrees F. Winter I have always found to be too cold and dry for chemical strippers to really work well.
If the wood has no sealer underneath, using only chemicals will tend to grind the pigment into the pores.
A hot stripper is always more satisfactory because it quickly lifts as much pigment out of the pores as possible.
Some people testify that brushing on a coat of shellac and then stripping again will pull more pigment out of the wood, the logic being that the paint will stick to the shellac; I can't verify this legend, but if you find yourself at an impasse, it's probably worth a halfhearted try.
Casey

Thanks, Casey. I have heard people mention a really good hot stripper, but I can't seem to recall the name of the one everyone raves about. Do you happen to know?

Silent paint remover?

By "Hot Stripper" I did not mean to imply:
Gypsy Rose Lee.
Any heat tools (heat gun, heat plate, silent paint stripper).
I did mean a chemical stripper with methylene chloride as the active ingredient, like (my fave) "Kutzit". The kind that smells and burns the skin, but works with amazing speed and gets the job done faster so you can enjoy your accomplishment.
A heat tool is great too, esp. if there is shellac underneath; so much better than chemicals alone.
Casey

have you tried the Peel Away Paint Stripper that you cover with paper. Paint sticks to paper with the stripper, very messy but works.

Here is a link that might be useful: Peel Away Paint Remover

I've never heard of that kind of stripper, sloyd. Thanks! I just might have to try that! :)

With seven kinds of 'peel away' it is pretty hard to make any judgement about the product.