Running a cold engine "hard " when it is cold should be avoided at all costs. At best it greatly accelerates wear,, at worse it can blow your engine. By hard, I mean both full throtle and or high RPMs while cold. Obviously the colder the engine the worse the scenario. On average a car can reach operating temperature within 3 miles of driving. When your temperature gauge reaches its normal temp, you should be good to go. There are two main reasons for this.
First, oil is most effective between 170 -220 degrees. Running it hard at 120 degrees, even though the oil has circulated will not completely protect your engine. F1 race cars pre-heat the engine and the oil before even starting an engine. They don't just do it for the heck of it.
Second reason, engine clearances. All the clearances of an engine are designed to run at normal operating temps. The clearances are not the same on a cold engine, and different metals expand at different rates until they reach their normal temp. Case in point, an aluminum block expands differently fom the rod bearings, which are different from the rods and pistons,and crankshaft etc. You get the point