I wouldn't advise it. I've had the same thought many a time, but knowing the speed of the current, even at it's slow point at Broadwater Bay, I wouldn't touch it. I'm assuming that's where you were looking? Even with ice picks or floats, I'd say too risky. If you know of a backwater channel somewhere with limited to no current (like a bay that touches the river and only flows in the spring at highwater), that'd be doable.
If you need to get out somewhere near town, head to Wadsworth or Pelican Point. Be careful at Wadsworth on the north side of the lake, I was walking around out there today, and it looks like some gas pockets popped through, the ice was all slushy and sketchy on top. If you're willing to drive, you could brave the wind and head to Frances, or hope the wind isn't blowing at Holter.