Umm, just say no. Adding a few inches in length to the narrow tread of a bike will not help near as much with traction as width. If you want to play on the ice without a fat tire bike, pick a sacrificial rear rim, an aggressive MTB tire, some flange head sheet metal screws, and a jumbo roll of gorilla tape. Oh and heavy duty tubes.
Bulk up the inside surface of the tire with two layers of Gorilla Tape. Don't use cheap ducktape, buy the good stuff. Run the screws through the tread from the inside, and cover the heads with a few more layers of tape. Install as normal, mindful of spikes. I recommend a lower pressure, so the tire squats a bit. TaDa!
Oh and gasbike sucks saggy green troll nuts
All just "opinion" as I would never be so foolish as to race anything on the ice and or snow, or even hot-rod at all... Says the Kaveman who treats his throttle like an on off switch...