Hey there...
Probably the top upgrade for snow and ice driving to improve traction (and safety) is to switch to winter tires. They are specificly designed for snow, slush, ice and low temperatures. Most folks choose to mount them on separate wheels instead of demounting and remounting with the season changes.
For example, a friend of mine lives in the Colorado mountains where they get 150+ inches of snow and lots of subzero temperatures. Heck, I was there a couple of summers ago and drove in 6-inches of snow in July when I climbed a pass a few miles away. Anyway, he drives a a nicely offroad modified 4wd truck but when winter hits, off come the BFG AT/KO tires (not a slouch in the winter in their own right) and on go the Nokian winter tires.
Slower is better when the ice and snow hit. It sounds like too much throttle may have been a factor in your first experiences with the MKZ? Front wheel drive is usually pretty good for straight ahead traction although it certainly will not stop any quicker so that can lead to a inaccurate sense of security.
Again though, tires are the main thing to focus on.
Hootowl