The icy moons of our solar system are prime candidates for hosting life. A thick outer ice shell and a subsurface ocean layer characterize these moons. To definitively establish the presence of life on these moons, in situ examination of the water beneath the ice shell is crucial. A promising technology to access this subsurface water is Melting probes, which enable thermal drilling [1]. To improve mission planning and optimize the design and operation of the melting probe, a digital twin can be developed and deployed. Cryotwin, a digital twin for melting probes, enables performance assessment across different operating scenarios [2,3,4]. At the heart of Cryotwin, a multi-physics model couples the contact-melting process with heat transfer and rigid-body motion [4] to assess the forward motion, efficiency, and melt channel radius of a thermal melting probe. Furthermore, Cryotwin provides the digital infrastructure to integrate environmental data and compute trajectories along with decision-relevant quantities of interest [4]. The performance of melting probes is influenced by the surrounding ice environment [1,5]. Accurate quantification of the ice environment is essential for accurate performance prediction. However, limited information about the ice environment necessitates uncertainty-informed performance analysis. Polynomial Chaos Expansion (PCE) provides a convenient way to perform sensitivity analysis and forward uncertainty quantification, and serves as a surrogate for the multi-physics model, enabling real-time calculations. In this contribution, we present the sensitivity analysis and forward uncertainty assessment conducted for the multi-physics model using PCE in Cryotwin. We evaluated the effect of the ice environment on the melting probe's performance under both terrestrial and icy-moon conditions. The density and temperature of the ice were found to be most sensitive and strongly influence the performance, underscoring the need to quantify them accurately.