A/T P tires in front, Highway LT's in back, any problem?

Does nobody remember "snow tires"? Back in the day most people, on most vehicles, ran rear tires that did not match the front for about half the year.
(On my pickups, snow tires in winter, then spring I would name them "Mud Grips")
As for different size F/R. 2 wheel drive, this is not a issue. 4 Wheel drive, can be a problem unless on surfaces you need 4 WD, and tires can slip