what do you mean by slowing down? do you mean braking? if so, it's probably worn bushes (anti-roll bar to tca). see here for a guide on how to replace them:
http://www.wrc-cosworth.org/howto/bushings.html

the abs is nothing to do with it. if it locks up straight away in the snow without any pedal pulsing, it's not working, but it can't cause 'shaking'