We analyze and explore the potential of using a polymer horizontal slot waveguide as light-analyte interactive region to implement a low-cost and highly sensitive liquid refractive index sensor. Numerical analysis shows that the optimized polymer horizontal slot waveguide is able to realize high waveguide sensitivity. With the optimized horizontal slot waveguide, polymer liquid refractive index sensors based on Mach-Zehnder interferometer (MZI) and microring resonator (MRR) are then investigated numerically, and the results show that the MZI-based sensor can achieve high sensitivity of 17024 nm/RIU and low limit of detection (LOD) of 1.76×10^-6 RIU while the MRR-based sensor can achieve the sensitivity of 177 nm/RIU and the LOD of 1.69×10^-4 RIU with a very small footprint. Compared with the sensors employing conventional silicon or silicon nitride vertical slot waveguide, the sensors employing polymer horizontal slot waveguide exhibit comparable performances but simpler and lower fabrication costs.