Yes that is perfectly normal
What you were hearing that clicking probably accompanied by your petal pushing back and fignting you was your anti-lock brakes working. (they only enguage and pump the brakes (40 times a second something like that) when they sence that they are begining to lock up). That is to say, the pump you felt really was a pump, it is an electric motor and pump that pumps the brakes way faster than humanly possible to keep them from locking up.
By the way, with anti-lock brakes you should allow even more stoping distance on ice as Anti-lock brakes actually take longer to stop than standard brakes on ice or loose gravel conditions. ABS brakes stop faster on wet, or dry pavement than standerd brakes. but their main funcion is to offer more control THey stop truer and streighter and offer more control in a stop (allow you to swerve if necessary) but, in icy conditions they do NOT stop faster than normal non Antilock power brakes
