Oxide heterointerfaces are ideal for investigating strong correlation effects to electron transport, relevant for oxide-electronics. Using hot-electrons, we probe electron transport perpendicular to the La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ (LSMO)- Nb-doped SrTiO$_3$ (Nb:STO) interface and find the characteristic hot-electron attenuation length in LSMO to be 1.48 $±$ 0.10 unit cells (u.c.) at -1.9 V, increasing to 2.02 $±$ 0.16 u.c. at -1.3 V at room temperature. Theoretical analysis of this energy dispersion reveals the dominance of electron-electron and polaron scattering. Direct visualization of the local electron transport shows different transmission at the terraces and at the step-edges. ; Comment: 15 pages, 4 figures