No cheat code spawns a horse. The PS2 version of The Sims 2 Pets has a limited cheat set (mostly motherlode, maxmotives, unlockcareerrewards via L1+R1+L2+R2 at neighborhood screen).
Money Tip: Use motherlode (L1+R1+L2+R2 → type) repeatedly for §50k each → Buy best horse + stall + gear immediately.