This paper presents a new Statistical Forward Planning (SFP) method, Rolling Horizon NeuroEvolution of Augmenting Topologies (rhNEAT). Unlike traditional Rolling Horizon Evolution, where an evolutionary algorithm is in charge of evolving a sequence of actions, rhNEAT evolves weights and connections of a neural network in real-time, planning several steps ahead before returning an action to execute in the game. Different versions of the algorithm are explored in a collection of 20 GVGAI games, and compared with other SFP methods and state of the art results. Although results are overall not better than other SFP methods, the nature of rhNEAT to adapt to changing game features has allowed to establish new state of the art records in games that other methods have traditionally struggled with. The algorithm proposed here is general and introduces a new way of representing information within rolling horizon evolution techniques.