An uninsulated air mattress will not provide very good insulation and may actually pull more heat away from you due to convection within the matress. You should look at an insulated matress or a couple of foam pads.

If your tent can not be properly pegged down then it may become a large kite if you get strong winds. A good bivy bag might work better for short term shelter in an exposed area. If there is snow then it is fairly easy to build a quick trench shelter in combination with your tarp and bivy bag. It helps to take a small snow shovel but make sure that it has a metal rather than plastic blade as the plastic blades are not very good at digging in old/compacted snow.

You should always try to get to shore and higher ground as cold air will settle in lower areas and you will be very exposed out on a lake.

When traveling over frozen water you should also have quick access to ice picks that you can use to help pull your self out if you break through the ice. It is also important to keep your extra clothing etc. in a waterproof bag in the event that you get wet.