The kagome metal compounds $A$V$_3$Sb$_5$ ($A$ = K, Rb, and Cs) feature a wealth of phenomena including nontrivial band topology, charge density wave (CDW), and superconductivity. One intriguing property is the time-reversal symmetry breaking in the CDW state without local moments, which leads to anomalous transport responses. Here, we report the investigation of magneto-thermoelectric effects on high-quality CsV$_3$Sb$_5$ single crystals. A large anomalous Nernst effect is observed at temperatures below 30 K. Multiple Fermi surfaces with small effective masses are revealed by quantum oscillations in Nernst and Seebeck signals under high magnetic field. Furthermore, we find an unknown frequency, and attribute it to the magnetic breakdown across two smaller Fermi surfaces. A gap around 20 meV can be resolved from the breakdown threshold field, which we propose to be introduced by the CDW. These results shed new light on the CDW-related phenomena, particularly in $A$V$_3$Sb$_5$ compounds.