Before a significant load is applied to the propulsion unit, a few areas that are sensitive - filling lifters & lifter bores, cylinder walls & piston skirts and bearings. Also, cheaper oil filters are not as robust when hit by cold high pressure oil. To the OP, I like to warm things up before the skier says hit it, my indicator is when the oil pressure starts to drop off the cold start up level, at that point I know everything has lubrication.
But - when the old one lap qualifying session was in effect in NASCAR, best power is with a cold air-fuel mixture so the teams pumped cold water through the engine just before the car went on the track and had the radiator covered so by the end of the lap it would be overheating and blowing steam out the vent. Note: these engines were specially built to handle it, so don't do this at home:-) On the flip side, there was an extensive start up routine (which included heating the oil) on the road race IMSA / Indy engines. The teams can't start the engines without a manufacturer tech monitoring the engine start up.