A pole-and-fabric construction on ice, not staked down, is called an iceboat. They have been clocked at over 100 mph. Whatever sort of tent you go with it needs to be securely attached if there's any chance of wind.
Ice climbing screws are designed for anywhere from maybe 400 pounds as rappel anchors to 1200 pound plus as leader protection. Tent guy-out points will surely fail at less than 100 pounds.
Ice is strong, and skinny Ti nails or hooks should hold fine if set at an appropriate angle. All you need is to pre-drill the hole.
Consider a Gimlet, Yankee Push Drill, or hand drill. I've had a Fiskars hand drill for 20 years and it works fine- though since it has plastic gears and crank it might not be a good choice for winter.
Here's a site that sells a set of 7 solid state "Steel Twist Gimlets" for under $20.
http://www.garrettwade.com/set-of-seven-steel-twist-gimlets/p/37J03.04/