Clouds strongly influence Earth's weather and climate, however they are difficult to model in computer simulations. Clouds containing ice are particularly hard to model since ice particles come in various shapes and sizes. To test the impact of ice complexity (e.g., shape), we run numerous simple climate simulations with identical set-ups, only varying three parameters related to ice complexity for each simulation. We call a collection of these simulations a perturbed parameter ensemble (PPE). From the PPE results, we find that parameters related to ice complexity have significant impacts on how much ice is formed in the atmosphere and how much energy is trapped or reflected by ice-containing clouds. This work shows how climate simulations are sensitive to certain 'knobs' in the model that are related to ice particle complexity, and gives us a path forward to tune these knobs to match real-world observations.