I would disagree with the basic premise that ABS should allow you to follow closer. ABS doesn't help with reaction time and its benefits on dry pavement are marginal.

But there are definite tactical differences to how you handle hard braking without ABS, and I would strongly agree with SoundsLikePuget's suggestion of practicing non-ABS hard braking. Also, if you ever happen to be somewhere with a big empty snowy parking lot, practicing skids at lower speeds can be very beneficial as well.

The biggest difference is on snow and ice. Just remember to tap your brakes, don't slam down the pedal. Besides if you grew up west of the Cascades you shouldn't be allowed to drive in snow anyway.

Well, You should always leave a safe distance between cars. If you always leave enough room to stop your alright. ABS brakes are most beneficial when in wet weather and when your on the brakes hard enough to skid. Drive safe.

Slight correction - the car in front of you can't stop faster. What they can do is stop straight. If you slam on your brakes, your car will most likely swerve as tires on one side or the other have more traction. Especially in wet weather, you have to learn the right technique (pumping the brakes) and know what a safe following distance is. Safe driving strategy for whatever vehicle you drive is always a good idea.