I would suggest two things. Studded tires, and better technique. First, you have massively increased the power in a lightweight car (generally a good thing for racing).
However, you will be in a constant fight for traction. Set yourself up with some extra tires on rims that you can swap out on the ice.
Second, you have minimal traction on ice and your tires' traction can only be used for one thing at a time- i.e. acceleration or steering or braking. If you expect to be able to brake while steering or steer while accelerating, you will be disappointed, especially in a front wheel drive.
I have been to several ice driving schools and the thing that impressed me most was that the line through corners was different than racing on pavement. On pavement the line is to start wide, clip the apex and accelerate wide out of the corner. On ice we were taught to do all of our braking in a straight line pulsing the pedal more rapidly as the car slows (with no steering inputs to upset things), slowly steer through the corner (using all the traction for steering) and to accelerate when the car was basically pointed in the right direction. Kicking the tail out is kinda fun but may not be the quickest way around the track in a front drive while you are learning.