NY, I have used chemical warmers on the bottom of my foot, and occasionally on top for many years. You may have to wear a slightly thinner wool sock (I have a lot of different thicknesses), but it works. Also, you have to ratchet your shoe a bit looser. The chemical warmers, with booties allowed me to ride in pretty cold temperatures and my regular shoes. Just remember to open the packet of warmers, and let them breathe for about 15 minutes before you put themin your shoes. They need air to activate. This why you need a little extra space in the shoes.
That said, I have had winter riding shoes for a couple of years. The ones for my road pedals are not as warm as the ones for my Frogs (on my other road bike). I occasionally use the heaters with them, but not as much as with regular shoes.
It was hard to find winter riding shoes in my small size (37) for road cleats. I got both pairs through an on-line store in the UK, for half price, at the end of the winter season. They have free shipping, too.