"4x4" and "all-wheel" drive are not the same thing, though misuse of the terms is making them increasingly meaningless.
"4x4" as it was used applied to "Jeeps" and trucks, later migrating to pickup trucks. One drive shaft ran from the transmission to a differential powering the rear wheels. On the side of the tranny was a PTO (power take off) with a shaft running to a front differential. It was never intended for use on pavement! Everyone knows, or should know, that differentials are required because in a turn the outside wheel turns faster than the inside wheel. One should also know that in a turn, the front wheels turn faster than the rear. With a "4x4" powering all 4 wheels, the front driveshaft spins at the same rate as the rear. When turning, the different speed of the front vs rear is taken up by tires slipping on mud, dirt, snow or something similar. On pavement with good traction, even intermittently so, a true 4x4 is very difficult to turn! Force the issue and the whole drive will buck if not break. Either a ditch trip or tow hook is a likely outcome for on street 4x4 use.
"All wheel drive" adds a third differential placed between the front a rear driveshafts which allows for powering all 4 wheels while on-road. Audi was the first to be commonly available with AWD, followed by Subaru (at half the price) and now many others.
Snow tires? Colorado tends to dry snow, Michigan to wet. Here, snow tires are magic, making my 2WD on snows roughly equivalent to my Audi Quattro on all-seasons.