Can any tire fit a 16 rim?

I have a 2012 Ford Escape with P235/70 R16. What I want to do is get a set of used rims to put winter tires on them so when seasons change, I can throw the tires on and be good. So can I just find any 16 rim and fit P235/60 tires on it?

No…
the R16 on the tire number is the radius they fit on BUT
the first number has to match as well
so a p210/70 R16 will not fit as the first number is the WIDTH of the rim/tire

the ONLY number that can change and have the tire still fit is the middle number. That is the aspect ratio of the tire (the ratio of how tall it is vs how wide it is)

Rims have different widths as well as diameters.
The tire needs to be suitable for both.
Rims also have different dtud patterns and offsets. These need to be suitable for the car as well as the width and diameter.

Sure

You need to make sure that the lug nut holes are drilled or made for a Ford.

If your car usually has the 235/70 and you change to 235/60 you will cause the following -
a - gearing will be lowered in all gears
b - the speedometer and odometer will both read higher than they did before at the same true speed/distance
c - the car will run nearly an inch lower on the road - in other words have around an inch less ground clearance.

No, it needs to be the correct width too. And what if your car had five studs, and the rim had four? Just make sure that you order a rim that goes with your car. Confirm that with whoever you buy it from. That's the best way.

If they are R15 then they will fit the rim but you need to know if the rims will fit your vehicle as the wheel nut patterns are not the same on every vehicle.