There is no way for us to ascertain whether or not 160 amps will do the job. It depends what your suv draws on severe use.
Usually a high end SUV with a tow package has all the bells and whistles. so on a rainy day you have the wipers on, engine running, heater on, defroster for the front and rear windows
and the mirror heaters. the seat warmers, the GPS and stereo systems and the fog lights
. The kids rear videos screens and maybe a movie going and the cell phones charging. now you add a larger alternator to power trailer usage because of modern luxuries sucking up all the juice. The larger alternator is usually built more robust since they are pulling larger loads.
Now you ask if the 160 amp alternator can do the same job. that depends on what your also willing to give up. even on a square trade saying that the 160 amp alternator is pulling 70% duty all the time and the 180 amp alternator is only pulling 50-60 % duty it going to last allot longer. the SUV with a tow package also is usually using a bigger engine to pull the load of both the trailer and larger alternator.
Then it all gets down to how its actually wired to get the juice you need at the trailer. If the wiring is too small for the amp draw you need you wont get the power nor will the regulator for the alternator sense you need more power and open up the charge rate for the battery
even if you have the biggest alternator available.
Is not a simple question if 160 amp or 180 amp alternator will work. Back in the old days we used 40 and 60 amp alternators and you really needed a 100 amp alternator when you added more amenities and fuel injection to the engines. Then it became an energy race to the top.
Just not a simple question to answer.