Traction control (TC) plays a key role in improving vehicle safety, especially for driving scenarios involving extremely low levels of tyre-road friction. In this paper a novel deep reinforcement learning (DRL) based TC strategy is formulated and its performance is compared against a nonlinear model predictive control (NMPC) solution for a simulated straight-line acceleration manoeuvre on icy road conditions. The paper explores the design and assessment of the proposed controllers using a vehicle model experimentally validated on ice. The simulation results show that the DRL solution outperforms the NMPC strategy by reducing the wheel slip ratio peaks and oscillations at the start of an acceleration manoeuvre. Additionally, it converges more quickly to the reference slip and is more computationally efficient.