Multi-hop Knowledge Graph Question Answering (KGQA) is a task that involves retrieving nodes from a knowledge graph (KG) to answer natural language questions. Recent GNN-based approaches formulate this task as a KG path searching problem, where messages are sequentially propagated from the seed node towards the answer nodes. However, these messages are past-oriented, and they do not consider the full KG context. To make matters worse, KG nodes often represent pronoun entities and are sometimes encrypted, being uninformative in selecting between paths. To address these problems, we propose Neural Tree Search (NuTrea), a tree search-based GNN model that incorporates the broader KG context. Our model adopts a message-passing scheme that probes the unreached subtree regions to boost the past-oriented embeddings. In addition, we introduce the Relation Frequency-Inverse Entity Frequency (RF-IEF) node embedding that considers the global KG context to better characterize ambiguous KG nodes. The general effectiveness of our approach is demonstrated through experiments on three major multi-hop KGQA benchmark datasets, and our extensive analyses further validate its expressiveness and robustness. Overall, NuTrea provides a powerful means to query the KG with complex natural language questions. Code is available at https://github.com/mlvlab/NuTrea.