One, you should match the rims. If you have 15 inch rims, then the snow rims should be 15 inch unless the tire size makes up for it...but why 14 inch on a 15 inch rim car? On my RAV it complained when I started using a different brand tire and I had to reset the TPMS to allow for that. Yes, it can be that sensitive. Your ABS may or may not complain. If you have discrete sensors in each rim then I'm sure it will set a code somewhere if the car doesn't sense them. You'll either have a warning light or the tire low light on most likely.
Under
most cases when using snow tires you will go down a rim size as you will in
most cases be using a tire with a taller sidewall... And narrower too; tall narrow tires work better in snow than fat. This was one reason that my Ural did so well on the snow covered roads...
ABS unless very specialized to the rim for unique reasons could care less the rim or tire used. What if the owner decided to install tires with a slightly different profile or size? That would be a huge mess that I would only expect from the likes of VW, BMW or Audi etc....