Your profile does not say where you are from, so a lot of this may not so much apply if you are in a popluated area, don't have to navigate any bush trails, don't get much snow, have cell phone coverage.....
Most of my fishing is done off of a snowmachine, but early and late in the ice season I do use a 4-wheeler and take all the same equipment, including the usual fishing items. A small rescue shovel (handle retracts, nice for clearing snow around holes or digging out), axe, small limb saw, jump starter, Masdam rope winch, length of rope, an 18" piece of metal fence post with a ring attached to put down in a ice hole to use as an anchor to winch too, vice grips, small crescent wrench, straight and phillips screw drivers, zip ties, towels to dry your hands, GPS, extra batteries, fold-up director's chair, communications device. This is a lot of stuff, but at one time or the other I use it all.
I wear my float suit all the time if there is even a question about the ice, I fell through 3 years ago and it did hold me up, I am a believer, the suits do work but won't do you much good sitting in a bucket.