s for snapping, that never seems to work that well
Just double click on the yellow center point. It gets blue. Klick on one of the most downward points of the object. Double click on the blue center point. It's yellow again. The center point which snaps to the surface will now align as you wish.
This method is ok, but with complex, small models it's sometimes tedious to get the right point. It doesn't work with subdivided models.
Sometimes at least, snapping does not work really well with surfaces (i. e it doesn't seem to register all of them). If that happens, try it again after changing the pivot a second time.
With subdivided models you have to do it by eye in cheetah, except when the border of the bottom is defined as 'crease' (selection, toogle crease). Otherwise you'd have to freeze the model, i. e. make editable, to use proper snapping.
"drop to floor" command in Poser
Actually it does nothing else then bring the most downward point of the object in contact with the surface. So if a the feet, or one, of a figure are not at an right angle, it could be, that the heel or a toe is this point that touches the ground.
The 'floor' (or 'ground') in any 3d app is 0 y. Always (only it wasn't always called y in earlier times). But there are several programs out there where you can put an object on the first surface it finds downward on the y-axis. That would be even better than just 'put on floor'.
I set up my default scene to have the ground a few units below 0 on the Y-axis just so that my figures's feet would land on it and not go through it when I use "drop to floor."
It's quiet a time since I used poser (was version 6), but something like this was never necessary. You just should make certain that the feet are in the right position – which they are not, when you have the problems you describe.
To be able to change the floor (or ground, ground plane etc) doesn't seem useful to me at all. Your problem wouldn't be solved as the object would still seem to hoover over the ground with the same position of the feet.
Well, another reason of your prob could be shoes. If you drop a figure to the floor it would align the feet, not the shoes. Their soles would be under the floor (but one the other hand, in more then 10 years they should have found a better solution for that. So I'm not sure, if that is your problem).
All in all it's often not that important if an object is not exactly on the surface of the floor. The most downward point can be somewhere in the middle and it would not look naturally as the borders of such an object wouldn't touch the floor.
All in all it's not a very important feature for cheetah. It can wait (there are some other problems to solve and more important features to build).