is 3.5 mil thick plastic sheeting thick enough to use for a backyard ice rink?
That should be fine. It's not the plastic, its the temperature. If its cold enough, the water will freeze even if you just flood the grass, on a cheap tarp, etc.
I would use one of those blue plastic tarps. You will get a few years use out of it. Lay your ice rink out using a line level, this way you willl not get any supprises as you start flooding the tarp. Flood it in stages, not all at once. For some reason this makes for stronger ice.
If you can capture enough water within that plastic, certainly! The head pressure of water is determined by it's depth and not by it's surface area. The ice will take all the weight of the skaters. Just be sure that you have enough depth of ice! I'm guessing that a little more than an inch or two will be fine.
for a few bucks more you can use ,and re- use next year 6 mil poly ,,,,,spend a little and save alot next year ....... good luck and remember the water will seek level so if your on any sort of hill / incline you better have a high enough board on the low end ~! happy skating ~!!
6 mil plastic sheeting at your hardware store is cheaper than 3.5 mil sheets bought at Walmart -- go figure