In the pursuit of achieving autonomous driving, ensuring comfortable and efficient handling of the vehicle is of paramount importance. One way to meet these requirements is by utilizing controllable suspensions as an active system. However, designing an effective control strategy requires knowledge of specific dynamical states, such as suspension stroke speed and displacement. The present study proposes a multi-horizon Virtual Sensor (VS) capable of estimating these states in order to address this issue. The VS is intended to replace or enhance limited direct measurement, and it is designed to cope with predictive control systems where future finite-horizon states are necessary. Importantly, the suggested approach is model-free and based on state-of-the-art deep forecasting models. The benchmark of the chosen models was conducted based on real experimental tests and evaluated using multiple metrics. Our study improves previous work in several aspects, including the use of a minimal instrumentation setup, accurate tracking performance over multiple horizons, the ability to explain the predictions, and the provision of confidence intervals for the estimated states.