The increasing demand for applications of the Internet of Things (IoT) has produced the emergence of use cases with challenging scenarios for cellular access. In such use cases, Low Earth Orbit (LEO) small satellite constellations provide global coverage for regions isolated from terrestrial infrastructure, but pose difficulties for routing given their dynamic nature. In this paper, we study ad hoc distance vector routing for LEO small satellite constellations. We provide a qualitative evaluation based on performance metrics such as scalability, robustness and energy consumption. Then, we propose Ad hoc On-Demand Distance Vector (AODV) as an applicable protocol and compare it with flooding with an implementation of a network simulator in C# for various constellation sizes and routing options. Our results show that routing across the constellation seam and the active route timeout play a critical role in the Packet Delivery Ratio (PDR) and packet throughput. Although reasonably functional, we conclude that AODV should be complemented with proactive routing in tightly controlled polar constellations, since pre-computed routing tables will perform better under specific conditions.