Magic School Bus says that weather works when warm, moisture-laden air rises into the air, forming clouds. As the clouds ascend, the moisture in them forms ice crystals, which descend to earth as ice or snow. However, as warm air moves, cold air moves in to vacate the area in question, unless there's enough warm, moist air (like in tropical areas) to keep the cold air at bay. Gotta love Ms. Frizzle, who is definitely a high-level Wizard. Shikka shikka ka-boom!
However, with your spells, you're taking warm, dry, desert air and attempting to transform it into cold, moist air, which, I'm not sure, is something the spell does, even with Cold Snap applied first.
But supposing you allowed it, and the game mechanics serviced drama as would a copper piece harlot, then yes. As your warm fronts and cold fronts met you'd have violent inward/upward winds and large cloud banks. But snow and ice wouldn't last past the spell's area.